Chapter 12, Problem 6CST

To determine

To find: The measure of an exterior angle of a regular pentagon.

Answer to Problem 6CST

The measure of an exterior angle of the regular pentagon is ${72}^{\circ }$ .

Explanation of Solution

Given information: A regular pentagon.

Calculation: Since, The sum of the exterior angles of any polygon is ${360}^{\circ }$ .

Therefore, The sum of the exterior angles of a pentagon is ${360}^{\circ }$ .

Now, The measure of an exterior angle of the regular pentagon is,

  $\begin{array}{l}=\frac{{360}^{\circ }}{5}\\ ={72}^{\circ }\end{array}$

Hence, The measure of an exterior angle of the regular pentagon is ${72}^{\circ }$ .