Chapter 11.3, Problem 4MRE

To determine

To Complete: If the measure of each exterior angle of the regular polygon is $20$ then the polygon has ….sides.

Answer to Problem 4MRE

  $18$

Explanation of Solution

Given: If the measure of each exterior angle of the regular polygon is $20$ then the polygon has ….sides.

Let $\theta$ be the exterior angle for $n$ sided regular polygon.

Then

  $\begin{array}{l}n\theta =360\\ n(20)=360\\ n=\frac{360}{20}\\ n=18\end{array}$

Hence, if the measure of each exterior angle of the regular polygon is $20$ then the polygon has $18$ sides.