Chapter 12, Problem 19CR

To determine

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

Answer to Problem 19CR

Therefore, the measure of an interior angle of regular octagon is ${135}^{\circ }$ and the measure of an exterior angle of a octagon is ${45}^{\circ }$ .

Explanation of Solution

Given information : Here, the polygon is regular octagon.

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

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. $n=8$

Therefore, the measure of an interior angle of regular octagon is

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

The measure of an exterior angle of a regular octagon is

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