Angles — Paper 2 · IGCSE Mathematics - International 0607

3 A 36° NOT TO SCALE x° B C AB = AC. Find the value of x. x = … [2]

2 marks

Mark scheme: 3 72 2 180 − 36 M1 for 2

This question in 0607/23 Oct/Nov 2017

7 The interior angle of a regular polygon is 160°. Find the number of sides of this polygon. … [3]

3 marks

Mark scheme: 7 18 3 360 M2 for oe 180 − 160 or M1 for 180 − 160

This question in 0607/23 Oct/Nov 2017

2 (a) Find, by measuring, the size of this reflex angle. … [1] (b) 80° NOT TO SCALE x° Work out the value of x. x = … [1] (c) Find the size of one exterior angle of a regular 18-sided polygon. … [2]

4 marks

Mark scheme: 2(a) 232 to 236 1 2(b) 100 1 2(c) 20 2 360 M1 for oe 18 If 0 scored SC1 for 160 seen

This question in 0607/21 May/June 2018

2 NOT TO SCALE x° 41° 76° A B AB is a straight line. Find the value of x. x = … [1]

1 marks

Mark scheme: 2 63 1

This question in 0607/22 May/June 2018

2 NOT TO SCALE x° 132° 156° Find the value of x. x = … [1]

1 marks

Mark scheme: 2 72 1

This question in 0607/21 Oct/Nov 2018

7 Find the size of one exterior angle of a regular octagon. … [2]

2 marks

Mark scheme: 7 45 2 6 M1 for 360 ÷ 8 or 180 − × 180 8

This question in 0607/21 Oct/Nov 2018

13 The bearing of point B from point A is 234°. Work out the bearing of point A from point B. … [2]

2 marks

Mark scheme: 13 [0]54 2 M1 for 234 − 180

This question in 0607/21 Oct/Nov 2018

3 A NOT TO 64° SCALE F 33° E 55° B C D ABC is a triangle. FED and BCD are straight lines. Work out angle EDC. Angle EDC = … [2]

2 marks

Mark scheme: 3 28 2 B1 for CED = 33 or ECD = 119 or ECB = 61 or BFD = 97

This question in 0607/21 May/June 2019

2 A regular polygon has 40 sides. Find the size of one exterior angle. … [2]

2 marks

Mark scheme: 2 9 2 360 M1 for 40

This question in 0607/22 May/June 2019

3 132° NOT TO SCALE 71° x° Find the value of x. x = … [2]

2 marks

Mark scheme: 3 61 2 M1 for 180 − 132 or M1 for 132 − 71

This question in 0607/23 May/June 2019

4 Each interior angle of a regular polygon is 170°. Find the number of sides of this polygon. … [3]

3 marks

Mark scheme: 4 36 3 360 M2 for 180 − 170 or M1 for 180 – 170

This question in 0607/22 Oct/Nov 2019

6 A 28° NOT TO SCALE x° B C AB = AC Find the value of x. x = … [2]

2 marks

Mark scheme: 6 76 2 M1 for (180 − 28) ÷ 2

This question in 0607/22 Oct/Nov 2019

6 Triangle ABC is isosceles and angle A = 40°. Find the three possible values for angle B. … , … , … [2]

2 marks

Mark scheme: 6 40, 70, 100 2 B1 for any two.

This question in 0607/23 Oct/Nov 2019

6 NOT TO SCALE 3x° 4x° 2x° A B AB is a straight line. Find the value of x. x = … [2]

2 marks

Mark scheme: 6 20 2 180 M1 for 2 + 3 + 4

This question in 0607/22 May/June 2020

9 The interior angle of a regular polygon is 150°. Find the number of sides of this polygon. … [3]

3 marks

Mark scheme: 9 12 3 360 M2 for oe 180 − 150 or M1 for 180 − 150

This question in 0607/22 May/June 2020

12 56° A NOT TO SCALE y° C B In the diagram, A, B and C are points on parallel lines. AC = BC . Work out the value of y. y = … [3]

3 marks

Mark scheme: 12 68 3 M1 for correct use of parallel lines to give a correct angle at B or C. M1 for correct use of isosceles triangle

This question in 0607/23 Oct/Nov 2020

9 NOT TO SCALE A 84° B The diagram shows part of polygon A and part of polygon B. A is a regular polygon with n sides. B is a regular hexagon. Find the value of n. n = … [3]

3 marks

Mark scheme: 9 15 3 B1 for 120° or 60° M1 for 360 = n(84 – their 60) or better ( n − 2)180 or = 360 – (84 + their 120) n

This question in 0607/22 May/June 2021

5 NOT TO SCALE x° 50° 60° Find the value of x. x = … [1]

1 marks

Mark scheme: 5 160 1

This question in 0607/23 May/June 2021

7 Find the size of one interior angle of a regular polygon with 20 sides. … [3]

3 marks

Mark scheme: 7 162 3 360 180(20 − 2) M2 for 180 − or 20 20 360 or M1 for or 180(20 – 2) oe 20

This question in 0607/23 May/June 2021

8 (a) A regular polygon has 12 sides. Work out the sum of the interior angles of the polygon. … [2] (b) The interior angle of a regular polygon is x°. Find an expression, in terms of x, for the number of sides of this polygon. … [2]

4 marks

Mark scheme: 8(a) 1800 2 M1 for (2 × 12 − 4) × 90 or (12 − 2) × 180 oe 8(b) 360 2 M1 for 180 −x or 180 n − 360 = nx 180 −x

This question in 0607/23 Oct/Nov 2021

6 Find the exterior angle of a regular polygon with 15 sides. … [2]

2 marks

Mark scheme: 6 24 2 M1 for 360 / 15 OR B1 for 156

This question in 0607/23 May/June 2022

2 A regular polygon has 24 sides. Find the size of each interior angle of the polygon. … [3]

3 marks

Mark scheme: 2 165 3 360 (24 − 2)180 M2 for 180 – or 24 24 360 or M1 for or (24 – 2) × 180 24

This question in 0607/22 Oct/Nov 2022

1 125° m° NOT TO k° SCALE The diagram shows a straight line intersecting two parallel lines. Find the value of k and the value of m. k = … m = … [2]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1 [k =] 125 2 B1 for each [m =] 55

This question in 0607/23 Oct/Nov 2022

4 NOT TO SCALE 3x° 3x° 2x° The diagram shows three angles on a straight line. Find the value of x. x = … [2]

2 marks

Mark scheme: 4 22.5 oe 2 M1 for 8x = 180 oe

This question in 0607/22 Feb/March 2023

9 The size of one exterior angle of a regular polygon is 24°. Find the number of sides of this polygon. … [2]

2 marks

Mark scheme: 9 15 2 360 M1 for oe 24

This question in 0607/22 Feb/March 2023

5 12 11 1 NOT TO 10 2 SCALE 9 3 8 4 7 5 6 The clock shows the time 09 30. Work out the obtuse angle between the hands of the clock. … [2]

2 marks

Mark scheme: 5 105 2 360 B1 for or 30 [for 1 hour] 12 or 15 [for half an hour] or 255 seen

This question in 0607/22 May/June 2023

2 NOT TO SCALE x° 64° 37° Find the value of x. x = … [1]

1 marks

Mark scheme: 2 79 1

This question in 0607/23 May/June 2023

1 105° NOT TO SCALE x° The diagram shows a straight line crossing two parallel lines. Find the value of x. x = … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 105 1

This question in 0607/21 Oct/Nov 2023

6 A NOT TO SCALE C B The diagram shows part of a regular hexagon, A, and part of a regular polygon, B. C is a square. Find the number of sides of the regular polygon, B. … [4]

4 marks

Mark scheme: 6 12 4 B2 for 150 (allow 60 + 90) or 30 or B1 for 120 and 90 M1 for 360 = (180 – their 150)n oe ( n − 2)  180 or = their150 oe n

This question in 0607/22 Feb/March 2024

6 A regular polygon has 12 sides. Find the size of an exterior angle of this polygon. … [2]

2 marks

Mark scheme: 6 30 2 360 (12 − 2)  180 M1 for or or for 12 12 150 seen

This question in 0607/21 Oct/Nov 2024

9 The interior angle of a regular polygon is 160°. Work out the number of sides for this polygon. … [3]

3 marks

Mark scheme: 9 18 3 M2 for 360 oe or 180( n − 2) = 160 n 180 − 160 or M1 for n − 2 180 − 160 or  180 = 160 n

This question in 0607/22 Oct/Nov 2024

4 A regular polygon has 20 sides. Work out the size of one interior angle of the polygon. … [3]

3 marks

Mark scheme: 4 162 3 360 180(20 − 2) M2 for 180 − or 20 20 360 or M1 for or 180 (20 – 2) 20

This question in 0607/23 May/June 2025

16 (a) Show that the interior angle of a regular hexagon is 120°. [1] (b) B NOT TO 15 cm SCALE A 10 cm The diagram shows a container in the shape of a prism. The cross-section of the prism is a regular hexagon with side length 10 cm. The height of the prism is 15 cm. A stick has one end at A and rests against B. The stick makes an angle of x with the base. Find tan x. tanx = … [4]

5 marks

Mark scheme: 16(a) 360 ÷ 6 or 180(6 – 2) 1 16(b) 15 4 M1 for angle x clearly indicated on oe diagram 20 B2 for diagonal of base = 20 10 10 or M1 for or cos60 sin30

This question in 0607/21 Oct/Nov 2025