Interior and Exterior Angles of Regular Polygons

In this worksheet, students apply their knowledge of triangles 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

Difficulty level:

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Worksheet Overview

The following formulae for regular polygons should be known:

Exterior angle = 360º ÷ number of sides

Interior angle = 180º - exterior angle

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

Example

A regular polygon has an interior angle of 165.6º.

How many sides does it have?

Answer

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

No. of sides = 360 ÷ exterior angle = 360 ÷ 14.4 = 25

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Preview activity

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