  # Interior Angles of Regular Polygons

In this worksheet, students calculate the interior angle of regular polygons. Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive/Use the Sum of Angles for Deduction

Difficulty level:   #### Worksheet Overview

Regular polygons have interior angles which are all equal to each other.

To work out the sum of the interior angles of a polygon, we first work out the sum of its angles by splitting it into triangles.

We then divide this sum by the number of angles.

Example

Work out the interior angle of a regular hexagon.

The hexagon can be split into triangles. There are 4 triangles inside the hexagon.

4 x 180º = 720º

The sum of the interior angles of a hexagon is 720º.

There are 6 equal angles inside the hexagon.

Each interior angle is 720º ÷ 6 = 120º

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