Angles in polygons

Polygons are two dimensional shapes with straight sides.

They can be described by the number of sides they have and whether the shape is regular or irregular.

Where the straight sides of the polygon meet, an angle is created. Angles are measured in degrees (°).

The internal angles of a triangle add up the 180° and the internal angles of a quadrilateral add up to 360°.

Complete this interactive activity to better understand how to calculate angles in a polygon. Then put your knowledge to the test.

It’s possible to work out the angles of polygons with more than 4 sides by cutting them up into triangles.

This is a regular hexagon. It has 6 sides and it can be divided into 4 triangles, like this:

You know that the sum of the internal angles of a triangle always add up to 180°.

So the combined total of 4 triangles would be:

180° + 180° + 180° + 180° = 720°

Therefore, you know that the sum of the internal angles of a hexagon is 720°.

To work out the value of each angle, you divide can divide this total by the number of angles.

There are 6 internal angles in a hexagon. So:

720° ÷ 6 = 120°

Therefore, each angle in a regular hexagon is 120°.

Example 2

Example 3