Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Find Missing Angles Using the Rules of Polygons

In this worksheet, students will apply their knowledge of interior and exterior angle rules of polygons to find missing angles.

'Find Missing Angles Using the Rules of Polygons' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Apply the Properties of Angles

Difficulty level:  

Worksheet Overview

In this activity, we will be looking at angle problems involving the rules of polygons.


Let's recap what we know already!


A regular polygon  - has sides that are all the same length and angles that are all equal. 


regular polygons


Make a note of the following formulae for regular polygons: 


Exterior angle = 360º ÷ number of sides


So with the octagon, each exterior angle is 360 ÷ 8 = 45º


exterior angles of an octagon


Interior angle = 180º - exterior angle


So, with an octagon, the interior angle is 180 - 45 = 135º


angles on straight line


Sum of interior angles = 180 x (number of sides - 2)


So with an octagon, the sum of the interior angles is 180 x (8 - 2) = 180 x 6 = 1,080º


Let's have a look at a typical question using this information.



A regular polygon has an interior angle of 165.6º

How many sides does it have?


angles on straight line




Exterior angle = 180 - interior angle = 180 - 165.6 = 14.4º

Number of sides = 360 ÷ exterior angle = 360 ÷ 14.4 = 25

So this regular polygon must have 25 sides.


Let's have a go at some questions now.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started

Try an activity or get started for free

  • National Tutoring Awards 2023 Shortlisted / Parents
    National Tutoring Awards 2023 Shortlisted
  • Private-Tutoring-WINNER-EducationInvestor-Awards / Parents
    Winner - Private Tutoring
  • Bett Awards Finalist / Parents
  • Winner - Best for Home Learning / Parents
    Winner - Best for Home Learning / Parents