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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.

'Interior and Exterior Angles of Regular Polygons' worksheet

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive and Illustrate Properties of Plane Figures

Difficulty level:  

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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