# How do i solve this question?Find the size of each exterior angle of a regular octagon.

Jun 24, 2018

45

#### Explanation:

The total sum of interior angles of any polygon is given by $180 \left(n - 2\right)$ where n is the number of sides

If your polygon is a octagon, that means you have 8 sides so n=8

The total sum of interior angles is then equal to $180 \left(8 - 2\right) = 1080$
Now since you want to find the value of your exterior angle, we first need to find the value of your interior angle.

Since we already found that the total value of your interior angle is equal to 1080, we divide 1080 by the number of angles which is 8
$\frac{1080}{8} = 135$

Because your interior angle is equal to 135 and the total sum of your exterior and interior angles are equal to 180 (angle on a straight line), your exterior angle is equal to $\textcolor{red}{180 - 135 = 45}$

Jun 24, 2018

${45}^{\circ}$

#### Explanation:

$\text{the sum of the exterior angles of a polygon is } {360}^{\circ}$

$\text{for a polygon of side n}$

$\text{exterior angle } = {360}^{\circ} / n$

$\text{here } n = 8$

$\text{exterior angle } = {360}^{\circ} / 8 = {45}^{\circ}$