  # Find the Interior and Exterior Angles of Regular Polygons

In this worksheet, students will apply their knowledge of formulae to calculate the interior and exterior angles of regular polygons. Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive and Illustrate Properties of Plane Figures

Popular topics:   Angles worksheets, Geometry worksheets

Difficulty level:   #### Worksheet Overview

In this activity, we will be looking at regular polygons.

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

As in this regular octagon below: The following formulae for regular polygons should be known:

Exterior angle = 360º ÷ number of sides

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

Interior angle = 180º - exterior angle

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

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

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

Example

A regular polygon has an interior angle of 165.6º

How many sides does it have?

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.

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