Skip to content

Paper Together: sit a paper in a room with your friends.See how it works

Angles in polygons practice questions with answers

Foundation and Higher · Grade 4 · Non-calculator

A second set of angles in polygons questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

A regular polygon has 9 sides. Work out the size of one exterior angle.

Show answer

Answer: 40

  1. The exterior angles of any polygon add to 360°.
  2. One exterior angle = 360° ÷ 9.
  • Method (1): The exterior angles of any polygon add to 360°.
  • Accuracy (1): Answer 40

Question 2 Easy

Work out the sum of the interior angles of a polygon with 17 sides.

Show answer

Answer: 2700

  1. A polygon with 17 sides splits into 17 − 2 = 15 triangles.
  2. The angles in each triangle add to 180°.
  • Method (1): A polygon with 17 sides splits into 17 − 2 = 15 triangles.
  • Accuracy (1): Answer 2700

Question 3 Medium

Four of the interior angles of a pentagon are 94°, 105°, 83° and 101°. Work out the size of the remaining angle.

Show answer

Answer: 157

  1. Interior angles of a pentagon add to (5 − 2) × 180° = 540°.
  2. The given angles add to 383°.
  • Method (1): Interior angles of a pentagon add to (5 − 2) × 180° = 540°.
  • Accuracy (1): Answer 157

Question 4 Medium

A regular polygon has 5 sides. Work out the size of one exterior angle.

Show answer

Answer: 72

  1. The exterior angles of any polygon add to 360°.
  2. One exterior angle = 360° ÷ 5.
  • Method (1): The exterior angles of any polygon add to 360°.
  • Accuracy (1): Answer 72

Question 5 Hard

Each exterior angle of a regular polygon is 90°. How many sides does the polygon have?

Show answer

Answer: 4

  1. The exterior angles of any polygon add to 360°.
  2. Number of sides = 360 ÷ 90.
  • Method (1): The exterior angles of any polygon add to 360°.
  • Accuracy (1): Answer 4

Question 6 Hard

Four of the interior angles of a pentagon are 112°, 121°, 102° and 114°. Work out the size of the remaining angle.

Show answer

Answer: 91

  1. Interior angles of a pentagon add to (5 − 2) × 180° = 540°.
  2. The given angles add to 449°.
  • Method (1): Interior angles of a pentagon add to (5 − 2) × 180° = 540°.
  • Accuracy (1): Answer 91

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Each exterior angle of a regular polygon is 36°. How many sides does the polygon have?

Show answer

Answer: 10

  1. The exterior angles of any polygon add to 360°.
  2. Number of sides = 360 ÷ 36.
  3. 360 ÷ 36 = 10.
  • Method (1): The exterior angles of any polygon add to 360°.
  • Accuracy (1): Answer 10

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

A regular polygon has 6 sides. Work out the size of one exterior angle.

  1. 60
  2. 30
  3. 120
Show answer

60 The result is 60.

Check 2

Work out the sum of the interior angles of a polygon with 18 sides.

  1. 2880
  2. 3240
  3. 3060
Show answer

2880 The result is 2880.

Check 3

A regular polygon has 8 sides. Work out the size of one interior angle.

  1. 135
  2. 45
  3. 1080
Show answer

135 The result is 135.

Check 4

Each exterior angle of a regular polygon is 72°. How many sides does the polygon have?

  1. 5
  2. 2.5
  3. 288
Show answer

5 The result is 5.

Check 5

Five of the interior angles of a hexagon are 120°, 119°, 119°, 112° and 113°. Work out the size of the remaining angle.

  1. 137
  2. 583
  3. 317
Show answer

137 The result is 137.

Check 6

A regular polygon has 20 sides. Work out the size of one exterior angle.

  1. 18
  2. 9
  3. 162
Show answer

18 The result is 18.

Check 7

Work out the sum of the interior angles of a polygon with 17 sides.

  1. 2700
  2. 3060
  3. 2880
Show answer

2700 The result is 2700.

Check 8

A regular polygon has 8 sides. Work out the size of one interior angle.

  1. 135
  2. 45
  3. 1080
Show answer

135 The result is 135.

Check 9

Each exterior angle of a regular polygon is 15°. How many sides does the polygon have?

  1. 24
  2. 12
  3. 345
Show answer

24 The result is 24.

Check 10

Five of the interior angles of a hexagon are 107°, 109°, 122°, 121° and 102°. Work out the size of the remaining angle.

  1. 159
  2. 561
  3. 339
Show answer

159 The result is 159.

Check 11

A regular polygon has 3 sides. Work out the size of one exterior angle.

  1. 120
  2. 122
  3. 130
Show answer

120 The result is 120.

Check 12

Work out the sum of the interior angles of a polygon with 14 sides.

  1. 2160
  2. 2520
  3. 2340
Show answer

2160 The result is 2160.

Check 13

A regular polygon has 6 sides. Work out the size of one interior angle.

  1. 120
  2. 60
  3. 720
Show answer

120 The result is 120.

Check 14

Each exterior angle of a regular polygon is 72°. How many sides does the polygon have?

  1. 5
  2. 2.5
  3. 288
Show answer

5 The result is 5.

Check 15

Five of the interior angles of a hexagon are 111°, 121°, 127°, 129° and 108°. Work out the size of the remaining angle.

  1. 124
  2. 596
  3. 304
Show answer

124 The result is 124.

Keep going with Angles in polygons

Practise free

Start free

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Next topicPractise free