# Each exterior angle of a regular polygon is 45°. What is the sum of the interior angles of the polygon?

Sep 21, 2016

The sum of the interior angles of the polygon is ${1080}^{o}$

#### Explanation:

Sum of exterior angle of any polygon is ${360}^{o}$.

As each exterior angle is ${45}^{o}$, number of angles or sides of the polygon is ${360}^{o} / {45}^{o} = 8$.

Further as each exterior angle is ${45}^{o}$, each interior angle is ${180}^{o} - {45}^{o} = {135}^{o}$.

As there are $8$ interior angles each ${135}^{o}$

the sum of the interior angles of the polygon is ${135}^{o} \times 8 = {1080}^{o}$