Chapter 6.1, Problem 35PPS

To determine

The measure of each exterior angle of a regular polygon.

Answer to Problem 35PPS

The measure of each exterior angle of a regular pentagon is 72.

Explanation of Solution

Given:

The given polygon is a pentagon.

Calculation:

The sum of the measures of exterior angles of a convex polygon, one angle at each vertex is 360.

Also, in a regular pentagon, there are 5 congruent interior angles.

The exterior angles of a pentagon are also congruent as angles supplementary to congruent angles are also congruent.

Suppose, the measure of each exterior angle be n.

Therefore,

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

The measure of each exterior angle of a regular pentagon is 72.