Chapter 11.5, Problem 34PPS

To determine

To calculate: The measure of an exterior angle of a regular 15-gon.

Answer to Problem 34PPS

The measure of an exterior angle of a regular 15-gon = ${24}^o$

Explanation of Solution

Given information: A regular 15-gon given. Sum of all the exterior angles of a regular polygon is ${360}^0$ .

Formula used: The measure of an exterior angle of a regular polygon = $\frac{{360}^o}{n}$ , when n = number of sides of the polygon.

Calculation:

We know that, sum of all the measures of a regular polygon is ${360}^o$ .

In a 15-gon, the total number of sides = 15.

So here, n = 15.

The measure of an exterior angle of a regular 15-gon = $\frac{{360}^o}{n}=\frac{{360}^o}{15}={24}^o$