# The sum of interior angles of polygons

To find the sum of the interior angles in a polygon, divide the polygon into triangles.

The sum of the angles in a triangle is 180°. To find the sum of the interior angles of a polygon, multiply the number of triangles in the polygon by 180°.

### Example

Calculate the sum of the interior angles in a pentagon.

A pentagon contains 3 triangles. The sum of the interior angles is:

${180}~\times~{3}~=~540^\circ$

The number of triangles in each polygon is two less than the number of sides.

The formula for calculating the sum of interior angles is:

$$({n}~-~{2})~\times~180^\circ$$ (where $${n}$$ is the number of sides)

Question

Calculate the sum of the interior angles in an octagon.

Using $$({n}~-~{2})~\times~180^\circ$$ where $${n}$$ is the number of sides:

$({8}~-~{2}) \times {180}~=~1,080^\circ$

### Calculating the size of each interior angle of regular polygons

All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle in a regular polygon is:

$$\text{interior~angle~of~a~regular~polygon}$$$$\text~=~\text{sum~of~interior~angles} \div \text{number~of~sides}$$

Question

Calculate the size of the interior angle of a regular .

The sum of the interior angles is $$({6}~-~{2})~\times~{180}~=~720^\circ$$

Each interior angle is $${720}~\div~{6}~=~120^\circ$$