Chapter 12.3, Problem 5E

To determine

To find : The measure of an exterior angle for the regular octagon.

Answer to Problem 5E

The measure of an exterior angle of a regular octagon is ${45}^{\circ }$.

Explanation of Solution

Given information : Here, the polygon is regular octagon.

Formula used :

All exterior angles of a regular polygon are equal and the measure of an exterior angle of regular n-gon is ${180}^{\circ }-\frac{\left(n-2\right)\times {180}^{\circ }}{n}$

Calculation :

Here, polygon is regular octagon i.e. $n=8$

The measure of an exterior angle of a regular octagon is

  $\begin{array}{l}{180}^{\circ }-\frac{\left(8-2\right)\times {180}^{\circ }}{8}\\ ={180}^{\circ }-\frac{6\times {180}^{\circ }}{8}\\ ={180}^{\circ }-\frac{{1080}^{\circ }}{8}\\ ={180}^{\circ }-{135}^{\circ }\\ ={45}^{\circ }\end{array}$

The measure of an exterior angle of a regular octagon is ${45}^{\circ }$