Chapter 7.4, Problem 7PSA

To determine

The name of the polygon is to be found

Answer to Problem 7PSA

The polygon is a pentagon

Explanation of Solution

Given information : The following statement has been told.

The measure of each exterior angle is $25\%$ the measure of each interior angle

We know that the exterior angle is given by

  $E=\frac{{360}^0}{n}$

While the interior angle is given by

  $I={180}^0-\frac{{360}^0}{n}$

And, we got

  $E=0.25I$

Hence, solving the linear equations, we get

  $n=5$

Hence, the polygon is a pentagon.