Interior Angle Sums

 You already know that the interior angles of a triangle add up to 180º.

 

Polygons with more sides have a larger sum of interior angles.

To work out the sum of the interior angles of a polygon with more sides, we choose one of the corners and split the polygon into triangles.  Each triangle will contain 180°.

 

Example

Work out the sum of the interior angles of this hexagon.

 

 

Answer

Choose any one corner.

 

 

Draw diagonals from the chosen corner to form triangles.

 

 

There are 4 triangles inside the hexagon.

4 x 180° = 720°

 

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

 

General Rule:

When you have a shape with n sides, the number of triangles it can be split into is n-2

Once you have the number of triangles, we can simply multiply that by 180° to find the internal angles.

For example: A 5 sided shape can be split into 3 triangles, if you then multiply 3 by 180 you get that there are 540° in a 5 sided shape.