Angles — Paper 1 · IGCSE Mathematics 0580

7 Reflex Right Acute Obtuse Use one of the above terms to describe each of the angles given. (a) 100o Answer(a) [1] (b) 200o Answer(b) [1]

2 marks

Mark scheme: 7 Obtuse 1 Reflex 1

This question in 0580/11 Oct/Nov 2004

13 A B C 35o D NOT TO SCALE E In the diagram BC is parallel to DE. ABD and ACE are straight lines. (a) Choose one of the following words to complete the statement in the answer space. congruent equilateral isosceles similar Answer (a) Triangle ABC and triangle ADE are [1] (b) Angle BDE = 35°. Calculate the size of angle DBC. Answer (b) Angle DBC = [1]

2 marks

Mark scheme: 13 (a) similar 1 (b) 145 1

This question in 0580/11 May/June 2005

10 Each interior angle of a regular polygon is 150°. For (a) Work out the size of each exterior angle. Examiner's Use Answer(a) [1] (b) Work out the number of sides of this polygon. Answer(b) [2]

3 marks

Mark scheme: 10 (a) 30 1 (b) 12 2ft M1 for 360 ÷ either 30 or their (a) ft. answer only when calculation gives an integer > 2

This question in 0580/11 Oct/Nov 2007

17 North North NOT TO 168° SCALE A C North 78° B The diagram shows the route of a fishing boat. The boat sails from A to B on a bearing 168° and then from B to C on a bearing 078°. AB = BC. (a) Show that angle ABC = 90°. Answer(a) [1] (b) Work out the bearing of C from A. Answer(b) [2]

3 marks

Mark scheme: 17 (a) 12 seen on diagram at A and B or 180o −168o= 12o. 1 Allow 168o + 12o = 180o only AND 12 + 78 (= 90) Allow 90o − 78o = 12o or 90o −12o = 78o if the first condition is satisfied (b) 123o 2 W1 for angle BAC (or angle BCA) = 45o

This question in 0580/11 Oct/Nov 2008

21 A cm 12 NOT TO SCALE B 68° D 8cm C 10 cm E In the diagram BC is parallel to DE. (a) Complete the following statement. Triangle ABC is to triangle ADE. [1] (b) AB = 12 cm, BC = 8 cm and DE = 10 cm. Calculate the length of AD. Answer(b) cm [2] (c) Angle ABC = 68°. Calculate the size of the reflex angle at D. Answer(c) [2]

5 marks

Mark scheme: 21 (a) Similar 1 (b) 15 2 M1 for 10 ÷ 8 × 12 or equivalent method (c) 292 2 M1 for 360 − 68

This question in 0580/11 Oct/Nov 2008

4 In the diagram AB is parallel to CD. For Examiner's Calculate the value of a. Use B NOT TO SCALE a° D A 5a° C Answer a = [2]

2 marks

Mark scheme: 4 30 2 M1 for a + 5a = 180 or 6a = 180 or 5a + 5a + a + a =360 or better

This question in 0580/11 May/June 2009

7 A and B are two points marked on a map. For Examiner's By measuring a suitable angle, find the bearing of A from B. Use North A North B Answer [2]

2 marks

Mark scheme: 7 328 ± 2 (ie 326 to 330) 2 W1 for angle of 32 ± 2 or 58 ± 2 or 148 ± 2 seen on diagram or in working or in the answer space. 2 2

This question in 0580/11 May/June 2009

18 For S Examiner's Use T NOT TO SCALE W 105° 38° P Q R The lines PS and QT intersect at W. PQR is a straight line. Angle SPR = 38° and angle TQR = 105°. Write down the size of the following angles. In each case give a reason for your answer. (a) Angle PQW = because [2] (b) Angle PWQ = because [2] (c) Angle TWS = because [2]

6 marks

Mark scheme: 18 (a) 75 Angle(s) (on a straight) line (=) 1, 1 Or reference to straight line and 180 180 (b) 67 Angle(s) (in a) triangle (sum to) 1ft,1 or exterior angle (of triangle is) sum of interior 180 (opposite) angles (c) 67 (vertically) opposite 1ft,1 IGCSE – October/November 2009 0580 11

This question in 0580/11 Oct/Nov 2009

19 ForFor Examiner'sExaminer's UseUse Silver Other Yellow Red The accurate pie chart shows information about the colours of 240 cars in a car park. (a) The sector angle for silver cars is 90°. Calculate the number of silver cars in the car park. Answer(a) [1] (b) There are 36 yellow cars in the car park. Showing all your working, calculate the sector angle for yellow cars. Answer(b) [2] (c) (i) Measure and write down the sector angle for red cars. Answer(c)(i) [1] (ii) Calculate the percentage of red cars in the car park. Answer(c)(ii) % [2]

6 marks

Mark scheme: 19 (a) 60 1 (b) 36 ÷ 240 × 360 oe M1 oe e.g. 36 × 90 ÷ 60 54 A1 W2 54 with some relevant working shown (c) (i) 116 to 118 1 (ii) 32.5 or their (c) (i) ÷ 3.6 2ft M1 for their (c) (i) ÷ 360 × 100 Or for their (c) (i) × (60 ÷ 90) ÷ 240 × 100 Allow revised angle in range 116 – 118 seen with working

This question in 0580/12 Oct/Nov 2009

1 Examiner's Use 157° NOT TO SCALE x° 84° Find the value of x. Answer x = [1]

1 marks

Mark scheme: Qu. Answers Mark Part Marks 1 119 1

This question in 0580/12 May/June 2010

North9 Examiner's Use D North North P H The positions of Perth (P), Darwin (D) and Hobart (H) are shown on the diagram. Measure accurately any angles you need and write down the bearing of (a) D from P, Answer(a) [1] (b) P from H. Answer(b) [1]

2 marks

Mark scheme: 9 (a) (0)34 to (0)36 1 (b) 286 to 289 1

This question in 0580/12 May/June 2010

1 Examiner's Use x° NOT TO SCALE 45° 26° Find the value of x. Answer x = [1]

1 marks

Mark scheme: Qu. Answers Mark Part Marks 1 109 1

This question in 0580/13 May/June 2010

12 Examiner's Use NOT TO SCALE 150° 150° The diagram shows part of a regular polygon with each interior angle 150°. Calculate the number of sides of the polygon. Answer [3]

3 marks

Mark scheme: 12 12 3 M1 for exterior angle 180 − 150 implied by 30 (could be on the diagram) and M1 dep for 360 ÷ their 30

This question in 0580/13 May/June 2010

20 For D C Examiner's Use 32° 67° NOT TO SCALE w° p° t° A B M The diagram shows a quadrilateral ABCD with DC parallel to AB. (a) Write down the geometrical name for a quadrilateral with only one pair of parallel sides. Answer(a) [1] (b) ABM is a straight line and DC = AC. Angle DCA = 32° and angle ACB = 67°. Find the values of p, t and w, giving a reason for each answer. Answer (b) p = because [2] t = because [2] w = because [2]

7 marks

Mark scheme: 20 (a) Trapezium 1 (b) p = 32°, alternate 1, 1 Accept Z angles t = 99°, exterior angle (of) triangle 1ft, 1 ft if t = p + 67 Accept angle of triangles and angles on straight line w = 74°, (base angle) isosceles triangle 1 , 1 Accept 12 (180 − 32 ) with isosceles

This question in 0580/11 Oct/Nov 2010

1 For x° 79° Examiner'sUse NOT TO SCALE 57° The diagram shows a quadrilateral. Work out the value of x. Answer x = [1]

1 marks

Mark scheme: Qu. Answers Mark Part Marks 1 134 1

This question in 0580/12 Oct/Nov 2010

9 North Q NOT TO SCALE North 840 m 65° P The diagram shows a straight road PQ. PQ = 840m and the bearing of Q from P is 065°. (a) Work out the bearing of P from Q. Answer(a) [1] 4 (b) Calvin walks of the distance from P to Q. 7 How far is he from Q? Answer(b) m [2]

3 marks

Mark scheme: 9 (a) 245 1 3 (b) 360 2 M1 for × 840 or 7 SC1 for answer 480 IGCSE – October/November 2010 0580 12 15

This question in 0580/12 Oct/Nov 2010

11 For C Examiner's NOT TO Use D SCALE 55° O A x° y° B The diagram shows a circle, centre O, with diameter BC. AB is a tangent to the circle at B and angle BCD = 55°. A straight line from A meets the circle at D and C. Calculate the value of (a) x, Answer(a) x = [2] (b) y. Answer(b) y = [1]

3 marks

Mark scheme: 11 (a) (x=) 35 2 B1 for angle BDC = 90 soi May be marked on the diagram (b) (y=) 55 1ft ft 90 − their x

This question in 0580/12 Oct/Nov 2010

9 For Examiner's Use A B 2x° NOT TO SCALE C D x° 5x° AB is parallel to CD. Calculate the value of x. Answer x = [3]

3 marks

Mark scheme: 9 22.5 oe 3 B2 for 180 = 5x + 2x + x oe or better B1 for 2x or 6x marked in the correct place on the diagram

This question in 0580/11 May/June 2011

18 For C Examiner's Use NOT TO SCALE O B 24° T A A, B and C are points on a circle, centre O. TA is a tangent to the circle at A and OBT is a straight line. AC is a diameter and angle OTA = 24°. Calculate (a) angle AOT, Answer(a) Angle AOT = [2] (b) angle BOC, Answer(b) Angle BOC = [1] (c) angle OCB. Answer(c) Angle OCB = [1]

4 marks

Mark scheme: 18 (a) 66° 2 M1 for 90° clearly identified as A (b) 114° 1ft 180 − their (a) 180 − their (b) their (a) (c) 33° 1ft or 2 2

This question in 0580/11 May/June 2011

2 x° NOT TO SCALE 52° A straight line intersects two parallel lines as shown in the diagram. Find the value of x. Answer x = [1]

1 marks

Mark scheme: 2 52 1

This question in 0580/12 May/June 2011

17 (a) What type of angle is shown by the arc on the diagram? Answer(a) [1] (b) ABCD is a quadrilateral. • AB is parallel to DC. • BC is longer than AD. (i) Draw a possible quadrilateral ABCD. Answer(b)(i) [1] (ii) Write down the geometrical name for the quadrilateral ABCD. Answer(b)(ii) [1]

3 marks

Mark scheme: 17 (a) Reflex 1 (b) (i) Drawing of a trapezium 1 Ignore labels and no arrows as long as a reasonable sketch. (ii) Trapezium 1 2

This question in 0580/13 May/June 2011

13 For Examiner's Use NOT TO SCALE The front of a house is in the shape of a hexagon with two right angles. The other four angles are all the same size. Calculate the size of one of these angles. Answer [3]

3 marks

Mark scheme: 13 135 cao 3 M1 for 720 or (6 – 2) × 180 oe seen in working and M1 for equation 180 + 4x = their 720 or M1 for (360 − 180) ÷ 4 (= 45) oe seen in working and M1 dep for 180 − their 45

This question in 0580/11 Oct/Nov 2011

16 (a) For C Examiner's Use 110° A B NOT TO SCALE D E In the diagram, AB is parallel to DE. Angle ABC = 110°. Find angle BDE. Answer(a) Angle BDE = [2] (b) NOT TO SCALE O y° B 50° z° t ° A T TA is a tangent at A to the circle, centre O. Angle OAB = 50°. Find the value of (i) y, Answer(b)(i) y = [1] (ii) z, Answer(b)(ii) z = [1] (iii) t. Answer(b)(iii) t = [1]

5 marks

Mark scheme: 16 (a) 70 2 B1 for angle ABD = 70° stated or seen on the diagram (b) (i) (y =) 80 1 (ii) (z =) 40 1 (iii) (t =) 10 1ft Follow through 90 − their y or 50 − their z IGCSE – October/November 2011 0580 11 2 2 ( )

This question in 0580/11 Oct/Nov 2011

10 For Examiner's Use 115° B E NOT TO SCALE y° x° A 20° D C In the diagram, AB is parallel to CDE. Find the value of (a) x, Answer(a) x = [1] (b) y. Answer(b) y = [2]

3 marks

Mark scheme: 10 (a) (x =) 20 1 (b) (y =) 65 2 B1 for ABD = 65° or ADB = 95°

This question in 0580/12 Oct/Nov 2011

11 NOT TO SCALE x° 75° 2x° 2x° (a) For the diagram above, write down an equation in x. Answer(a) [1] (b) Solve your equation. Answer(b) x = [2]

3 marks

Mark scheme: 11 (a) x + 2x + 2x + 75 = 360 1 Allow 4x + x + 75 = 360 or 5x + 75 = 360 or 5x = 285 (b) (x =) 57 cao 2 M1 correct first step after 5x + 75 = 360 ie 5x = 360 − 75 or x + 15 = 72 If zero SC1 for correct solution to their linear equation seen in part (a) or in part (b) if (a) is blank IGCSE – October/November 2011 0580 12 1 6 4 3 13 25

This question in 0580/12 Oct/Nov 2011

21 For D Examiner's Use C NOT TO SCALE 58° 40° A B In the quadrilateral ABCD, AB = AD and CB = CD. Angle BAD = 40° and angle CBD = 58°. (a) Calculate (i) angle ABD, Answer(a)(i) Angle ABD = [1] (ii) angle BCD. Answer(a)(ii) Angle BCD = [1] (b) Write down the mathematical name for the quadrilateral ABCD. Answer(b) [1]

3 marks

Mark scheme: 21 (a) (i) 70 1 (ii) 64 1 (b) Kite 1

This question in 0580/13 Oct/Nov 2011

7 (a) A quadrilateral has four sides of equal length and two pairs of equal angles. For Examiner's Write down the mathematical name for this quadrilateral. Use Answer(a) [1] (b) 92° NOT TO SCALE 74° 63° Three of the angles in a quadrilateral are 63°, 74° and 92°. Work out the size of the fourth angle. Answer(b) [1]

2 marks

Mark scheme: 7 (a) Rhombus 1 (b) 131° 1 2 7

This question in 0580/11 May/June 2012

15 (a) Find the value of x. For Examiner's Use NOT TO x° SCALE 51° Answer(a) x = [1] (b) EF is a diameter of the circle. Find the value of y. y° E 63° NOT TO SCALE F Answer(b) y = [1] (c) Find the value of z in this isosceles triangle. NOT TO 48° SCALE z° Answer(c) z = [1]

3 marks

Mark scheme: 15 (a) 51° 1 (b) 90° 1 (c) 66° 1

This question in 0580/11 May/June 2012

7 A 73° B NOT TO 120° SCALE 82° x° C D E The diagram shows a quadrilateral ABCD. CDE is a straight line. Calculate the value of x. Answer x = [2]

2 marks

Mark scheme: 7 95 2 B1 for 85 seen or M1 x = 180 – ‘their angle ADC’, if it is clearly seen

This question in 0580/13 May/June 2012

11 For E Examiner's D F Use b° 52° NOT TO SCALE a° A C B In the diagram lines AC and DF are parallel and AE = EB. Angle AEB = 52°. (a) Write down the mathematical name for triangle AEB. Answer(a) [1] (b) Work out the value of a. Answer(b) a = [1] (c) Explain why a = b. Answer(c) [1]

3 marks

Mark scheme: 11 (a) isosceles 1 (b) 64 1 (c) alternate (angle) 1 accept z angle IGCSE – May/June 2012 0580 13

This question in 0580/13 May/June 2012

3 NOT TO 36° SCALE x 87° 75° (a) Find angle x. Answer(a) Angle x = [1] (b) What type of angle is x ? Answer(b) [1]

2 marks

Mark scheme: 3 (a) 162 1 (b) obtuse 1

This question in 0580/11 Oct/Nov 2012

15 The diagram shows an isosceles triangle between two parallel lines. For Examiner's Use q° p° NOT TO SCALE 115° Calculate (a) the value of p, Answer(a) p = [2] (b) the value of q. Answer(b) q = [1]

3 marks

Mark scheme: 15 (a) 50 2 M1 for method of finding base angle of isosceles triangle (could be on diagram). (b) 65 1 ft 115 – their (a) or (180 – their (a)) ÷ 2 7 5 2 ($) 693 ( 00)

This question in 0580/12 Oct/Nov 2012

6 For Examiner's Use 50° NOT TO 55° SCALE a° Use the information in the diagram to fi nd the value of a. Answer a = … [2] _____________________________________________________________________________________

2 marks

Mark scheme: 6 105 2 M1 for 180 – 55 – 50 or B1 for 55 or 75 seen in the correct angle inside the triangle 3 k M1 f

This question in 0580/11 May/June 2013

13 Complete each statement with the correct mathematical term. For Examiner's Use (a) This solid is a … [1] (b) This polygon is a regular … [1] (c) A B C Angle ABC is an … angle [1] _____________________________________________________________________________________

3 marks

Mark scheme: 13 (a) cuboid 1 condone [rectangular] prism (b) pentagon 1 (c) obtuse 1

This question in 0580/11 May/June 2013

7 (a) Draw an acute angle. Label the acute angle with the letter a. [1] (b) Write down the mathematical name of angle b. b Answer(b) … [1] _____________________________________________________________________________________

2 marks

Mark scheme: 7 (a) Any acute angle with angle indicated 1 (b) Obtuse 1

This question in 0580/12 May/June 2013

15 (a) For Examiner′s Use 128° NOT TO SCALE x° A straight line intersects two parallel lines as shown. Find the value of x. Answer(a) x = … [2] (b) NOT TO 30° SCALE 128° y° Calculate the value of y. Answer(b) y = … [1] _____________________________________________________________________________________

3 marks

Mark scheme: 15 (a) 52 2 M1 for 180 – 128 or 128 or 52 marked on diagram in a correct position. (b) 22 1 5

This question in 0580/12 May/June 2013

11 B NOT TO O SCALE A 87° 63° 81° C D (a) Calculate the size of angle AOB. Answer(a) Angle AOB = … [1] (b) What type of angle is angle AOB? Answer(b) … [1] _____________________________________________________________________________________

2 marks

Mark scheme: 11 (a) 129 1 (b) Obtuse 1 IGCSE – May/June 2013 0580 13

This question in 0580/13 May/June 2013

9 For Examiner′s NOT TO Use SCALE 55° p° Find the value of p. Answer p = … [2] _____________________________________________________________________________________

2 marks

Mark scheme: 9 125 2 B1 for 55 or 125 in any other correct position on diagram or M1 for 180 – 55 IGCSE – October/November 2013 0580 11 17 5

This question in 0580/11 Oct/Nov 2013

13 Yim knows one angle of an isosceles triangle is 48°. He says one of the other angles must be 66°. Explain why Yim is wrong. Answer … … [2] _____________________________________________________________________________________

2 marks

Mark scheme: 13 [Other angle could be] 84 2 M1 for 180 – (48 + 48) or SC1 shows that two angles of 66 are needed to make an isosceles triangle 2

This question in 0580/11 Oct/Nov 2013

3 NOT TO SCALE x° 59° 163° (a) Find the value of x. Answer(a) x = … [1] (b) One of the angles is 163°. What type of angle is this? Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 3 (a) 138 1 (b) Obtuse 1

This question in 0580/11 May/June 2014

14 A E b° a° NOT TO SCALE 127° D C B The diagram shows an isosceles triangle ABC. DCB is a straight line and is parallel to AE. Angle DCA = 127°. Find the value of (a) a, Answer(a) a = … [2] (b) b. Answer(b) b = … [1] __________________________________________________________________________________________

3 marks

Mark scheme: 14 (a) 74 2 M1 Angle B = 180 – 127 (b) 53 1FT 127 – their part (a)

This question in 0580/11 May/June 2014

19 similar acute line perpendicular radius refl ex obtuse parallel congruent isosceles Choose the correct word from this box to complete each of these statements. (a) A Angle A is … [1] (b) B Angle B is … [1] (c) These lines are … [1] (d) These lines are … [1] __________________________________________________________________________________________

4 marks

Mark scheme: 19 (a) acute 1 (b) reflex 1 (c) parallel 1 (d) perpendicular 1 3

This question in 0580/12 May/June 2014

3 NOT TO 52° SCALE x° In the diagram, a straight line intersects two parallel lines. Find the value of x. Answer x = … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 3 128 1

This question in 0580/13 May/June 2014

21 Each exterior angle of a regular polygon is 30°. Work out the number of sides the polygon has. Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 21 12 2 M1 for 360 ÷ 30

This question in 0580/13 May/June 2014

4 B NOT TO SCALE C 98° A 105° k° In the diagram, all four lines are straight. Angle A = 105°, angle B = 90° and angle C = 98°. Find the value of k. Answer k = … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 4 113 2 M1 for 360 – (98 + 90 + 105) or better

This question in 0580/11 Oct/Nov 2014

19 C NOT TO D SCALE A z° 24° y° x° B E The points B, C, D and E lie on a circle. AB and AC are equal length tangents to the circle. BD is a diameter of the circle and BC is parallel to ED. Angle BDE = 24°. Calculate the value of (a) x, Answer(a) x = … [2] (b) y, Answer(b) y = … [1] (c) z. Answer(c) z = … [2] __________________________________________________________________________________________

5 marks

Mark scheme: 19 (a) [x =] 66 2 B1 for angle BED = 90° soi (b) [y =] 24 1 (c) [z =] 48 2FT M1FT for angle ABC = 90° − their y

This question in 0580/12 Oct/Nov 2014

20 D C E A B (a) Draw the locus of the points which are 3 cm from E. [1] (b) Using a straight edge and compasses only, construct the bisector of angle DCB. [2] (c) Shade the region which is ● less than 3 cm from E and ● nearer to CB than to CD. [1] __________________________________________________________________________________________

4 marks

Mark scheme: 20 (a) Complete circle centre E radius 3 cm 1 (b) Correct ruled bisector with two pairs of 2 B1 for correct bisector with no/wrong correct arcs arcs (c) 1 dep on attempt at bisector of C and enclosed region

This question in 0580/13 Oct/Nov 2014

22 This is an accurate drawing of quadrilateral ABCD. D C A B (a) Write down the mathematical name for quadrilateral ABCD. Answer(a) … [1] (b) Measure the size of the acute angle. Answer(b) … [1] (c) By taking suitable measurements from the diagram, work out the area of ABCD. Answer(c) … cm2 [3] __________________________________________________________________________________________

5 marks

Mark scheme: 22 (a) Trapezium 1 (b) 55o 1 (c) 21.4 or 19.55 to 23.37 nfww 3 B1 for [AB =] 7.2, [DC =] 4.7, and [height =] 3.6 seen and M1 for 5.0 × their 6.3 × their (7.4 + 2.7 )

This question in 0580/13 Oct/Nov 2014

3 Measure the reflex angle at B. B Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 3 332 or 330 to 334 1

This question in 0580/12 Feb/March 2015

15 (a) NOT TO 44° SCALE x° The diagram shows an isosceles triangle. Find the value of x. Answer(a) x = … [1] (b) (i) The exterior angle of a regular polygon is 24°. Find the number of sides of this regular polygon. Answer(b)(i) … [2] (ii) Write down the mathematical name for a 5-sided polygon. Answer(b)(ii) … [1] __________________________________________________________________________________________

4 marks

Mark scheme: 15 (a) 68 1 360 (b) (i) 15 2 M1 for = 24 or (n − 2 )180 = 156n n (ii) pentagon 1 25 25

This question in 0580/12 Feb/March 2015

7 equilateral triangle square regular pentagon parallelogram regular hexagon circle From the list write down (a) the shape which has more than 6 lines of symmetry, Answer(a) … [1] (b) the shape which has both acute and obtuse interior angles. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 7 (a) circle 1 (b) parallelogram 1

This question in 0580/11 May/June 2015

2 NOT TO 124° SCALE x° Find the value of x. Answer x = … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 2 56 1 22 88

This question in 0580/13 May/June 2015

11 D NOT TO 102° E SCALE 82° x° 64° A B C The diagram shows an isosceles triangle ABE and a quadrilateral BCDE. ABC is a straight line. Calculate the value of x. Answer x = … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 11 44 www 3 M1 for angle [EBC =] 360 – (82 + 102 + 64) oe or better M1FT for angle ABE = 180 – ‘their EBC’

This question in 0580/13 May/June 2015

13 A B C 120° 32° 64° NOT TO SCALE E D The diagram shows quadrilateral ACDE. AC is parallel to ED and B is a point on AC. Angle EAB = 120°, angle ABE = 32° and angle CBD = 64°. (a) Work out angle EBD. Answer(a) Angle EBD = … [1] (b) Work out angle AEB. Answer(b) Angle AEB = … [1] (c) Complete this statement. Angle BED = angle ABE because they are … angles. [1] __________________________________________________________________________________________

3 marks

Mark scheme: 13 (a) 84 1 (b) 28 1 (c) Alternate 1 360 180× (15 2) 90 ( 2 15 4)

This question in 0580/11 Oct/Nov 2015

14 Work out the size of one interior angle of a regular 15-sided polygon. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 360 180 × (15 − 2) 90 × ( 2 × 15 − 4) or or14 156 3 M2 for 180 − 15 15 15 360 or M1 for or 180 × (15 – 2) oe 15

This question in 0580/11 Oct/Nov 2015

18 This scale drawing shows the positions of two towns, A and B, on a map. North A B (a) Measure the bearing of town B from town A. Answer(a) … [1] (b) On the map, town C is 8 cm from town A on a bearing of 155°. Mark the position of town C on the scale drawing. [2] __________________________________________________________________________________________

3 marks

Mark scheme: 18 (a) 230 1 (b) C marked in correct position 2 B1 for correct distance 8 cm or correct bearing 155°

This question in 0580/13 Oct/Nov 2015

20 (a) The diagram shows a quadrilateral with one side extended. 98° NOT TO 112° SCALE 66° x° Find the value of x. Answer(a) x = … [2] (b) Find the sum of the interior angles of a 25-sided polygon. Answer(b) … [2] __________________________________________________________________________________________

4 marks

Mark scheme: 20 (a) 96 2 M1 for 360 – (66 + 98 +112)  360  (b) 4140 2 M1 for (25 – 2) × 180 or 25 ×  180 −   25  10

This question in 0580/13 Oct/Nov 2015

17 (a) x° NOT TO SCALE 47° Find the value of x. x = … [1] (b) 85° 115° NOT TO SCALE 97° y° Find the value of y. y = … [2]

3 marks

Mark scheme: 17 (a) 47 1 (b) 117 2 M1 for 360 − (115 + 85 + 97 ) 35( or 95) 39 35 k ( or 95 k ) 39 k

This question in 0580/12 Feb/March 2016

7 Write down the mathematical name for (a) an angle that is less than 90°, … [1] (b) a five-sided polygon. … [1]

2 marks

Mark scheme: 7 (a) Acute 1 (b) Pentagon 1  6 

This question in 0580/11 May/June 2016

14 C D 40° NOT TO SCALE b° a° A B Triangle ABC is isosceles and AC is parallel to BD. Find the value of a and the value of b. a = … b = … [2]

2 marks

Mark scheme: 14 [a =] 70 2 B1 for each [b =] 40

This question in 0580/11 May/June 2016

17 A regular polygon has an interior angle of 172°. Find the number of sides of this polygon. … [3]

3 marks

Mark scheme: 17 45 3 M2 for 360 ÷ (180 – 172) 180 ( n – 2 ) or M1 for 180 – 172 or = 172 oe n 21 3

This question in 0580/12 May/June 2016

15 NOT TO SCALE x° y° 42° The diagram is made from 5 congruent kites. Work out the value of (a) x, x = … [1] (b) y. y = … [2]

3 marks

Mark scheme: 15 (a) 72 1 (b) 123 2FT FT dep. on answer being obtuse M1 for (360 – their ( a ) – 42) [÷2]

This question in 0580/13 May/June 2016

10 67° NOT TO SCALE a° 42° Find the value of a. a = … [2]

2 marks

Mark scheme: 10 25 2 B1 for 67 or 113 seen once in correct position or M1 for a + 42 = 67 or a + 42 + 113 = 180 or better

This question in 0580/12 Oct/Nov 2016

20 (a) A NOT TO SCALE C 44° B Triangle ABC is an isosceles triangle with AB = CB. Angle ABC = 44°. Find angle ACB. Angle ACB = … [1] (b) A regular polygon has an exterior angle of 40°. Work out the number of sides of this polygon. … [2]

3 marks

Mark scheme: 20 (a) 68 1 (b) 9 2 M1 for 360 ÷ 40 oe or 180 ( n − 2 ) = 140 oe n

This question in 0580/13 Oct/Nov 2016

12 NOT TO p° 70° SCALE q° The diagram shows a straight line intersecting two parallel lines. Find the value of p and the value of q. p = … q = … [2]

2 marks

Mark scheme: 12 110 1 70 1

This question in 0580/12 May/June 2017

12 The three angles in a triangle are 5x°, 6x° and 7x°. 7x° NOT TO SCALE 6x° 5x° (a) Find the value of x. x = … [2] (b) Work out the size of the largest angle in the triangle. … [1]

3 marks

Mark scheme: 12(a) 10 2 180 M1 for 5 x + 6 x + 7 x = 180 oe or 5 + 6 + 7 or B1 for angles 50, 60 and 70 12(b) 70 1FT FT 7 × their (a) provided 0 < their answer < 180

This question in 0580/13 May/June 2017

1 NOT TO 72° 83° SCALE 104° x° The diagram shows a quadrilateral. Find the value of x. x = … [1]

1 marks

Mark scheme: Question Answer Marks Partial marks 1 101 1

This question in 0580/11 Oct/Nov 2017

15 The diagram shows a regular pentagon. A AB is a line of symmetry. d ° Work out the value of d. NOT TO SCALE B d = … [3]

3 marks

Mark scheme: 15 54 3 180 × (5 − 2) 360 M2 for or 180 − 5 5 360 or M1 for 180 × (5 − 2) or 5 √

This question in 0580/11 Oct/Nov 2017

9 NOT TO 80° SCALE 120° y° x° A B In the diagram, AB is a straight line. Find the value of x and the value of y. x = … y = … [2]

2 marks

Mark scheme: 9 [x =] 60 2 B1 for each [y =] 40 or for two numbers that add to 100

This question in 0580/12 Oct/Nov 2017

18 Find the size of the interior angle of a regular hexagon. … [3]

3 marks

Mark scheme: 18 120 nfww 3 360 180 × (6 − 2) M2 for 180 − oe 6 6 360 or M1 for soi by 60 6 or 180 × (6 − 2) soi by 720

This question in 0580/12 Oct/Nov 2017

3 The diagram shows a quadrilateral. x° NOT TO 47° 95° SCALE 82° Find the value of x. x = … [1]

1 marks

Mark scheme: 3 136 1

This question in 0580/11 May/June 2018

7 Q T A 43° C x° NOT TO SCALE P B S The diagram shows two parallel lines PAQ and SBCT. AB = AC and angle QAC = 43°. Find the value of x. x = … [2]

2 marks

Mark scheme: 7 94 2 B1 for ACB or PAB or ABC = 43 or M1 for 180 − 2 × 43 or 12 x = 90 − 43

This question in 0580/11 May/June 2018

14 Work out the size of one exterior angle of a regular octagon. … [2]

2 marks

Mark scheme: 14 45 2 360 M1 for 8 If zero scored, SC1 for answer 135

This question in 0580/11 May/June 2018

6 (a) Write down the mathematical name of the type of angle marked. … [1] (b) A and B are points on the circumference of a circle, centre O. O B A Write down the mathematical name of the line AB. … [1]

2 marks

Mark scheme: 6(a) acute 1 6(b) diameter 1

This question in 0580/13 May/June 2018

22 A B NOT TO x° SCALE 56° L M C y° N The diagram shows an isosceles triangle ABC with AB = AC. LCM and BCN are straight lines and LCM is parallel to AB. Angle ACL = 56°. Find the value of x and the value of y. x = … y = … [4] Question 23 is printed on the next page.

4 marks

Mark scheme: 22 [x = ] 62 2 B1 for 56 identified as angle A (180 − 56 ) or M1 for 2 [y = ] 118 2 FT for 2 marks their acute x + their y =180 or 56 + their acute x = their y or B1 for any of ACB, BCM or LCN = 62 or their acute x or M1 for 180 – 62 or 180 – their acute x or 56 + 62 or 56 + their acute x

This question in 0580/11 Oct/Nov 2018

1 Write down the type of angle shown in the diagram. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 Obtuse 1

This question in 0580/12 Oct/Nov 2018

19 (a) NOT TO x° 55° 42° SCALE 153° Find the value of x. x = … [1] (b) A 48° NOT TO SCALE y° B C D ABC is an isosceles triangle and BCD is a straight line. Find the value of y. y = … [2]

3 marks

Mark scheme: 19(a) 110 1 19(b) 114 2 M1 for (180 – 48) ÷ 2

This question in 0580/13 Oct/Nov 2018

3 A B C D Complete the statement. Angle … is a reflex angle. [1]

1 marks

Mark scheme: 3 C 1

This question in 0580/12 Feb/March 2019

6 A student measures the angles in a triangle as 55°, 85° and 50°. Explain why the student is incorrect. … [1]

1 marks

Mark scheme: 6 correct explanation 1 need to see 190 and 180

This question in 0580/12 Feb/March 2019

6 Complete each statement. (a) A quadrilateral with only one pair of parallel sides is called a … . [1] (b) An angle greater than 90° but less than 180° is called … . [1]

2 marks

Mark scheme: 6(a) Trapezium 1 6(b) Obtuse 1

This question in 0580/12 May/June 2019

8 a d b c e X f g The diagram shows two parallel lines and a straight line crossing them. Write down, using letters from a to g, (a) the angle that is alternate to angle X, … [1] (b) the angle that is corresponding to angle X. … [1]

2 marks

Mark scheme: 8(a) b 1 8(b) d 1

This question in 0580/12 May/June 2019

23 K J NOT TO E D SCALE O A C F B H G The diagram shows two regular pentagons. Pentagon FGHJK is an enlargement of pentagon ABCDE, centre O. Find angle AEK. Angle AEK = … [4]

4 marks

Mark scheme: 23 126 4 360 − 180 – ( 360 ÷ 5 )  M3 for or 2 360 − 180 × ( 5 − 2 ) ÷ 5 2 180 × ( 5 − 2 ) 360 or M2 for or 180 – 5 5 360 or M1 for 180 × (5 – 2) or 5

This question in 0580/13 May/June 2019

3 North A North B Measure the bearing of B from A. … [1]

1 marks

Mark scheme: 3 113° 1

This question in 0580/12 Oct/Nov 2019

1 Write down the mathematical name of this type of angle. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 acute 1

This question in 0580/13 Oct/Nov 2019

4 NOT TO SCALE 124° 107° x° Work out the value of x. Give a geometrical reason for your answer. x = … because … [2]

2 marks

Mark scheme: 4 129 2 B1 for each Angles at a point sum to 360 oe

This question in 0580/12 Feb/March 2020

14 The diagram shows a trapezium. ( 97 - 3x)° NOT TO SCALE ( 69 + 5x)° Work out the value of x. x = … [3]

3 marks

Mark scheme: 14 7 3 M2 for 166 + 2x = 180 or better or M1 for 97 – 3x + 69 + 5x = 180 oe

This question in 0580/11 May/June 2020

2 (a) Write down the mathematical name for this type of angle. … [1] (b) NOT TO B SCALE A O A and B lie on a circle, centre O. (i) Write down the mathematical name for line AB. … [1] (ii) OA = 8cm Write down the length of the diameter of this circle. … cm [1]

3 marks

Mark scheme: 2(a) Acute 1 2(b)(i) Chord 1 2(b)(ii) 16 1

This question in 0580/12 May/June 2020

8 B x° NOT TO 135° A 72° SCALE D y° 88° C In the diagram, AB is parallel to CD. (a) Find the value of x. Give a geometrical reason for your answer. x = … because … [2] (b) Work out the value of y. Give a geometrical reason for your answer. y = … because … [2]

4 marks

Mark scheme: 8(a) 72 2 B1 for each Corresponding angles 8(b) 65 2 B1 for each Angles [at a point] sum [to] 360 oe

This question in 0580/13 May/June 2020

1 Write down the mathematical name for (a) an angle which is less than 90°, … [1] (b) a polygon with 5 sides, … [1] (c) a quadrilateral with exactly one pair of parallel sides. … [1]

3 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Acute 1 1(b) Pentagon 1 1(c) Trapezium 1

This question in 0580/11 Oct/Nov 2020

10 x° y° NOT TO SCALE 140° 120° The diagram shows a triangle drawn between a pair of parallel lines. Find the value of x and the value of y. x = … y = … [3]

3 marks

Mark scheme: 10 [x =] 60 3 B1 for [x =] 60 [y =] 80 B2 for [y =] 80 or B1 for 40 in correct position in diagram If 0 scored, SC1 for their x + their y = 140

This question in 0580/12 Oct/Nov 2020

10 NOT TO 59° 37° SCALE a° c° b° The diagram shows two parallel lines intersected by two straight lines. Find the values of a, b and c. a = … b = … c = … [3]

3 marks

Mark scheme: 10 [a =] 59 3 B1 for each [b =] 37 If 0 scored, SC1 for [c =] 84 their (a + b + c) = 180 if a, b, c > 0

This question in 0580/11 May/June 2021

11 (a) Write down the mathematical name for a polygon with 5 sides. … [1] (b) Work out the interior angle of a regular 18‑sided polygon. … [2]

3 marks

Mark scheme: 11(a) Pentagon 1 11(b) 160 2 360 (18 − 2 ) × 180 M1 for 180 − or oe 18 18

This question in 0580/11 May/June 2021

22 4x° NOT TO SCALE ( 3x + 75 )° ( 87- )x° The diagram shows a quadrilateral. Work out the value of x. x = … [4]

4 marks

Mark scheme: 22 18 4 B3 for 6x = 108 or M2 for 4x + 3x + 75 + 87 – x + 90 =360 oe or better or M1 for 4x + 3x + 75 + 87 – x [+ 90] or better or M1 for 4x + 3x + 75 + 87 – x [+ 90] = k If zero scored, SC1 for ax = 108 (a ≠ 6) or for 6x = b (b ≠ 108)

This question in 0580/12 May/June 2021

1 a (a) Measure angle a. … [1] (b) Write down the mathematical name for this type of angle. … [1]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 144 to 148 1 1(b) Obtuse 1

This question in 0580/13 May/June 2021

5 x NOT TO SCALE 40° The diagram shows a pair of parallel lines and a straight line. Complete the statement with the correct geometrical reason. x = 40° because the angles are … [1]

1 marks

Mark scheme: 5 Corresponding 1

This question in 0580/13 May/June 2021

8 NOT TO SCALE 100° y° y° Find the value of y. y = … [2]

2 marks

Mark scheme: 8 130 2 M1 for 360 – 100 or better

This question in 0580/13 May/June 2021

14 The exterior angle of a regular polygon is 36°. Find how many sides this polygon has. … [1]

1 marks

Mark scheme: 14 10 1

This question in 0580/13 May/June 2021

9 The scale drawing shows the positions of two towns, P and Q. The scale is 1 cm represents 4 km. North Q North P Scale: 1 cm to 4 km (a) Find the actual distance between town P and town Q. … km [2] (b) Measure the bearing of town Q from town P. … [1] (c) Town X is 28 km from town P on a bearing of 140°. On the scale drawing, mark the position of town X. [2]

5 marks

Mark scheme: 9(a) 32.8 2 M1 for 8 [cm] to 8.4 [cm] seen or for their measurement [in cm] multiplied by 4 9(b) 065 1 9(c) X correctly placed 2 M1 for X on bearing of 140° from P 7 cm from P on a bearing of 140° or for X 7 cm from P If 0 scored, SC1 for X on bearing of 140 from Q and 7 cm from Q

This question in 0580/11 Oct/Nov 2021

3 Write down the mathematical name for this type of angle. … [1]

1 marks

Mark scheme: 3 Acute 1

This question in 0580/12 Oct/Nov 2021

18 A 86° B x° NOT TO SCALE C 58° D Triangle ABC and triangle ACD are isosceles. Angle DAB = 86° and angle ADC = 58°. Find the value of x. x = … [3]

3 marks

Mark scheme: 18 79 nfww 3 M2 for x + x + 58 + 58 + 86 = 360 oe or 86 – (180 – 2 × 58) implied by CAB = 22 or B1 for DCA = 58 or BCA = x or DAC = 64

This question in 0580/12 Oct/Nov 2021

13 x° NOT TO SCALE 132° The diagram shows two parallel lines intersecting a straight line. Find the value of x. x = … [2]

2 marks

Mark scheme: 13 48 2 B1 for 132 or 48 in the correct position on the diagram or M1 for 180 – 132

This question in 0580/13 Oct/Nov 2021

21 Find the interior angle of a regular 7-sided polygon. … [2]

2 marks

Mark scheme: 21 129 or 128. 6 or 128.57 to 128.57... 2 M1 for 180 – (360 ÷ 7) or (7–2) × 180 ÷ 7

This question in 0580/13 Oct/Nov 2021

8 (a) Measure the marked angle. … [1] (b) NOT TO 9.5 cm 8 cm SCALE 12 cm Using a ruler and compasses only, construct this triangle. Leave in your construction arcs. The side of length 12 cm has been drawn for you. [2]

3 marks

Mark scheme: 8(a) 40° 1 8(b) Correct triangle with arcs 2 B1 for correct triangle with incorrect or no arcs or for two correct arcs or for a triangle with arcs but one side not in range

This question in 0580/12 Feb/March 2022

4 The scale drawing shows the positions of town A and town B. The scale is 1 cm represents 15 km. North North B A Scale: 1 cm to 15 km (a) Find the actual distance between town A and town B. … km [2] (b) Measure the bearing of town B from town A. … [1]

3 marks

Mark scheme: 4(a) 111 [km] 2 M1 for 7.2[cm] to7.6[cm] seen or for their measurement [in cm] multiplied by 15 evaluated 4(b) [0]71 1

This question in 0580/11 May/June 2022

7 NOT TO y° SCALE x° 68° The diagram shows two parallel lines and a straight line crossing them. Find the value of x and the value of y. x = … y = … [2]

2 marks

Mark scheme: 7 112 68 2 B1 for each

This question in 0580/11 May/June 2022

6 North A North B Measure the bearing of point B from point A. … [1]

1 marks

Mark scheme: 6 142° 1

This question in 0580/13 May/June 2022

9 T NOT TO S SCALE R 73° 75° P 129° Q PQRS is a quadrilateral. RST is a straight line. Find angle PST. Angle PST = … [2]

2 marks

Mark scheme: 9 97 2 M1 for 360 – (73 + 129 + 75)

This question in 0580/13 May/June 2022

2 Write down the mathematical name of this type of angle. … [1]

1 marks

Mark scheme: 2 Obtuse 1

This question in 0580/11 Oct/Nov 2022

8 x° 71° NOT TO SCALE 55° The diagram shows two straight lines intersecting two parallel lines. Find the value of x. x = … [2]

2 marks

Mark scheme: 8 54 2 M1 for 180 – 71 – 55 oe or B1 for 55 or 125 in a relevant correct position on the diagram

This question in 0580/11 Oct/Nov 2022

7 x° NOT TO SCALE 34° The diagram shows an isosceles triangle. Find the value of x. x = … [2]

2 marks

Mark scheme: 7 112 2 M1 for 180 – 34 × 2 oe

This question in 0580/12 Oct/Nov 2022

10 a° a° a° a° a° Give the geometrical reason why the value of a is 72. … … [1]

1 marks

Mark scheme: 10 Angles [round a] point [add to] 360 1

This question in 0580/13 Oct/Nov 2022

24 NOT TO SCALE (7x + 44)° (x + 8)° The diagram shows two sides of a regular polygon. The interior angle of the polygon is ( 7x + 44) ° and the exterior angle is ( x + 8 )° . Find the number of sides of this polygon. … [4]

4 marks

Mark scheme: 24 15 4 B2 for x = 16 soi or M1 for 7x + 44 + x + 8 = 180 or better M1 for 360 ÷ (their x + 8) oe

This question in 0580/13 Oct/Nov 2022

12 (a) NOT TO SCALE 52° x° The diagram shows a pair of parallel lines and a straight line. Write down the geometrical reason why the value of x is 52. … [1] (b) NOT TO 126° SCALE 38° y° Find the value of y and write down the geometrical reason for your answer. y = … because … [2]

3 marks

Mark scheme: 12(a) Alternate angles 1 12(b) 196 2 B1 for each Angles at a point sum to 360

This question in 0580/11 May/June 2023

21 4x° NOT TO SCALE (3x - 1)° The diagram shows a right-angled triangle. Use the information in the diagram to write down and solve an equation to find the value of x. x = … [3]

3 marks

Mark scheme: 21 4x + 3x – 1 + 90 = 180 oe B1 13 2 M1 for 4x + 3x = 90 + 1 or better

This question in 0580/11 May/June 2023

5 B NOT TO 59° SCALE 73° x° y° A C D In the diagram, ABC is a triangle and ACD is a straight line. Find the value of x and the value of y. x = … y = … [2]

2 marks

Mark scheme: 5 [x= ] 48 2 B1 for each [y = ]132 If 0 scored, SC1 for two answers that add up to 180

This question in 0580/12 May/June 2023

12 A 38° NOT TO SCALE x° B C Triangle ABC is isosceles. Angle BAC = 38° and AB = AC. Find the value of x. x = … [2]

2 marks

Mark scheme: 12 71 2 180  38 M1 for 2

This question in 0580/13 May/June 2023

11 50° x° NOT TO SCALE 114° The diagram shows two straight lines crossing two parallel lines. Find the value of x. x = … [2]

2 marks

Mark scheme: 11 64 2 B1 for any of these angles labelled on the diagram. M1 for 114 – 50 or better

This question in 0580/12 Oct/Nov 2023

13 North NOT TO North SCALE P 39° Q East Find the bearing of Q from P. … [2]

2 marks

Mark scheme: 13 231 2 B1 for any of these angles in correct place on the diagram 51 or 129 or 141 between east line drawn from P to PQ or 39 between west line dawn from P to PQ or indicating the correct bearing of Q from P on the diagram. or M1 for 180 + (90 – 39) oe or 360 – (90 + 39)

This question in 0580/12 Oct/Nov 2023

9 NOT TO SCALE x° x° The diagram shows an equilateral triangle. Find the value of x. x = … [2]

2 marks

Mark scheme: 9 150 2 M1 for 360 – 60

This question in 0580/13 Oct/Nov 2023

14 B NOT TO 112° SCALE 44° C M A The diagram shows triangle ABC. M is the midpoint of AC. Triangle ABC is rotated 180° about centre M. The image and the original triangle together form a quadrilateral ABCD. (a) Write down the mathematical name of the quadrilateral ABCD. … [1] (b) Find angle BAD. Angle BAD = … [2]

3 marks

Mark scheme: 14(a) Parallelogram 1 14(b) 68 2 M1 for 180 – 112 or for 180 – 112 – 44 oe

This question in 0580/13 Oct/Nov 2023

2 C B x A (a) Measure the size of angle x. … [1] (b) Measure the length of line AB in millimetres. … mm [1] (c) Mark the midpoint, M, of line AB. [1] (d) Draw a line through the point M that is perpendicular to line AB. [1]

4 marks

Mark scheme: 2(a) 46° 1 2(b) 84 1 2(c) Mid-point marked 42 mm along AB from A. 1 2(d) Line at 90° to AB at M. 1 FT their mid-point

This question in 0580/12 May/June 2024

11 x° NOT TO SCALE 36° The diagram shows an isosceles triangle. Find the value of x. x = … [2]

2 marks

Mark scheme: 11 108 2 M1 for 180 – 36 – 36 oe

This question in 0580/13 May/June 2024

3 x (a) Measure angle x. Angle x = … [1] (b) Write down the mathematical name for this type of angle. … [1]

2 marks

Mark scheme: 3(a) 83 1 3(b) Acute 1

This question in 0580/11 Oct/Nov 2024

8 NOT TO SCALE 28° 138° 49° y° The diagram shows a quadrilateral. Find the value of y. y = … [2]

2 marks

Mark scheme: 8 61 2 M1 for [reflex = ]360 – 138 oe or for 138 – 49 – 28 oe

This question in 0580/11 Oct/Nov 2024

9 The diagram shows an isosceles triangle. x° NOT TO SCALE 43° Find the value of x. x = … [2]

2 marks

Mark scheme: 9 94 2 M1 for x + 2 × 43 = 180 oe

This question in 0580/12 Oct/Nov 2024

12 The scale drawing shows the positions of two ships, A and B. The scale is 1 cm represents 6 km. North A Scale : 1 cm to 6 km B (a) Measure the bearing of ship B from ship A. … [1] (b) Find the actual distance between the two ships. … km [2]

3 marks

Mark scheme: 12(a) 143 1 12(b) 39 2 B1 for 6.5 or M1 for their 6.5 × 6

This question in 0580/12 Oct/Nov 2024

17 The diagram shows a parallelogram. (132 – 2x)° NOT TO SCALE (15 + 5x)° Work out the size of the smallest interior angle of the parallelogram. … [4]

4 marks

Mark scheme: 17 70 4 B3 for x = 11 OR M1 for 132 – 2x + 15 + 5x = 180 oe M1 for collecting x terms on one side and number terms on the other for their equation. M1 for 15 + 5 × their x oe where –3 < their x < 15 or for 132 – 2 × their x oe where 21 < their x < 66

This question in 0580/12 Oct/Nov 2024

9 The scale drawing shows the positions of town K and town L. The scale is 1 cm represents 10 km. North L North K Scale : 1 cm to 10 km (a) Find the actual distance between town K and town L. … km [2] (b) Measure the bearing of town L from town K. … [1] (c) Town M is 40 km from town L on a bearing of 140°. On the scale drawing, mark the position of town M. [2]

5 marks

Mark scheme: 9(a) 85 2 B1 for 8.5 or M1 for their 8.5 × 10 9(b) 065 1 9(c) M in correct position 2 B1 for a correct length, 4cm or B1 for a correct bearing, 140º

This question in 0580/13 Oct/Nov 2024

11 (a) NOT TO SCALE 80° w° The diagram shows three lines meeting at a point. Find the value of w. w = … [1] (b) D 80° NOT TO SCALE y° A B C BCD is an isosceles triangle. ABC is a straight line. Work out the value of y. y = … [3]

4 marks

Mark scheme: 11(a) 190 1 11(b) 130 3 B2 for DBC or BCD = 50 or M2 for 180 – ((180 – 80) ÷ 2) oe or M1 for (180 – 80) ÷ 2

This question in 0580/13 Oct/Nov 2024

15 Find the size of an interior angle of a regular 15-sided polygon. … [2]

2 marks

Mark scheme: 15 156 2 180  (15 – 2 ) M1 for 180 – 360 ÷ 15 oe or oe 15

This question in 0580/13 Oct/Nov 2024

15 D NOT TO SCALE y° A B C The diagram shows a triangle BCD and a straight line ABC. DB=DC=BC. (a) Write down the mathematical name for triangle BCD. … [1] (b) Work out the value of y. Give two geometrical reasons for your answer. y = … because 1. … 2. … [4]

5 marks

Mark scheme: 15(a) equilateral 1 15(b) 120 2 B1 for DBC=60 Angles in an equilateral triangle are 1 equal Angles on a straight line add to 180 1

This question in 0580/12 Feb/March 2025

4 The diagram shows a line AB and a point P. A P B (a) Measure the length of line AB in millimetres. … mm [1] (b) Draw a line through point P that is perpendicular to line AB. [1]

2 marks

Mark scheme: 4(a) 83 1 4(b) ruled perpendicular line through P 1

This question in 0580/12 May/June 2025

2 (a) Write down the mathematical name for an angle between 90° and 180°. … [1] (b) Write down the mathematical term that describes two polygons that are the same shape and size. … [1]

2 marks

Mark scheme: 2(a) Obtuse 1 2(b) Congruent 1

This question in 0580/13 May/June 2025

4 The diagram shows a quadrilateral with sides of equal length. NOT TO SCALE a° 2a° (a) Write down the mathematical name for this quadrilateral. … [1] (b) Work out the value of a. a = … [2]

3 marks

Mark scheme: 4(a) Rhombus 1 4(b) 60 2 M1 for a + 2a = 180 oe or better

This question in 0580/13 May/June 2025

13 The scale drawing shows the positions of town A and town B. The scale is 1 centimetre represents 10 kilometres. North B North A Scale: 1 cm to 10 km (a) Work out the actual distance from town A to town B. … km [2] (b) Measure the bearing of town B from town A. … [1] (c) Town C is 45 km from town A on a bearing of 310°. On the scale drawing, mark the position of town C. [2]

5 marks

Mark scheme: 13(a) 80 2 B1 for 8 or M1 for their 8 × 10 13(b) 032 1 13(c) Point correctly plotted 2 B1 for distance 4.3 to 4.7 cm from A or B1 for bearing 308º to 312º from A

This question in 0580/11 Oct/Nov 2025

15 D NOT TO x° SCALE 140° A B C ABC is a straight line and ABD is an isosceles triangle. Work out the value of x. x = … [3]

3 marks

Mark scheme: 15 100 3 M2 for 180 – (180 –140) × 2 oe or M1 for 180 – 140 or for 180 – (2 × their 40)

This question in 0580/11 Oct/Nov 2025

12 The diagram shows a parallelogram. ( 3x + 10 ) ° NOT TO SCALE ( x - 30 ) ° (a) Use the information in the diagram to write an equation and solve it to find the value of x. x = … [4] (b) Find the value of the largest angle in this parallelogram. … [1]

5 marks

Mark scheme: 12(a) 4x = 200 oe M3 M2 for x – 30 + 3x + 10 = 180 oe M1 for attempt to simplify to ax − b = c or ax = b + c OR If M0 scored M2 for correct simplification to ax = b + c FT from their linear equation or M1 for correct simplification to ax − b = c FT from their linear equation OR If M0 award SC2 for answer of 50 from no working or from no incorrect working 50 A1 12(b) 160 nfww 1 FT 3 × their 50 + 10

This question in 0580/12 Oct/Nov 2025

22 Work out the size of one interior angle of a regular hexagon. … [2]

2 marks

Mark scheme: 22 120 2 M1 for 180 − (360 ÷ 6) oe or ( 6 − 2 )  180 oe 6

This question in 0580/12 Oct/Nov 2025

3 a (a) Measure angle a. … [1] (b) Write down the mathematical name of this type of angle. … [1]

2 marks

Mark scheme: 3(a) 123 1 3(b) Obtuse 1

This question in 0580/13 Oct/Nov 2025

10 x° 40° NOT TO SCALE y° The diagram shows an isosceles triangle between a pair of parallel lines. (a) Find the value of x. x = … [2] (b) Find the value of y. Give a geometrical reason for your answer. y = … because … … [2]

4 marks

Mark scheme: 10(a) 70 2 180 − 40 M1 for oe 2 10(b) 110 1 FT 180 – their (a) Angles on a straight line add to 180 oe 1 nfww

This question in 0580/13 Oct/Nov 2025

19 Find the number of sides of a regular polygon with interior angle 160°. … [2]

2 marks

Mark scheme: 19 18 2 360 M1 for 180 −160 180 ( n − 2 ) or for = 160 n

This question in 0580/13 Oct/Nov 2025

24 (a) The scale on a map is 1 cm represents 12 km. Write this in the ratio 1 : n . 1 : … [1] (b) The bearing of B from A is 070°. Find the bearing of A from B. … [2]

3 marks

Mark scheme: 24(a) 1 200 000 1 24(b) 250 2 M1 for 70 + 180 or correct diagram indicating angle

This question in 0580/13 Oct/Nov 2025