Chapter 11.3, Problem 34IP

To determine

To find the measure of an exterior angle of a regular decagon.

Answer to Problem 34IP

  ${36}^0$

Explanation of Solution

Given:

A regular decagon.

Formula used:

Exterior angle of a given polygon: $\frac{{360}^0}{n}$ where $n$ is the number of sides of the polygon.

Calculation:

In case of a regular decagon, $n=10.$

Now according to the formula of finding the measure of exterior angle of a polygon,

  $\Rightarrow \frac{{360}^0}{n}$

Now putting $n=10$ ,

  $\Rightarrow \frac{{360}^0}{10}={36}^0$

  $\Rightarrow {36}^0$

Conclusion:

Therefore, the measure of an exterior angle of an equilateral triangle is ${36}^0$ .