Chapter 7.4, Problem 11PSB

To determine

The name of the polygon is to be found

Answer to Problem 11PSB

The name of the polygon is Pentagon

Explanation of Solution

Given information : The following statement has been given

The sum of a polygon’s angle measure is nine times the measure of an exterior angle of a regular hexagon.

We know that the sum of an exterior angle of a regular hexagon is

  $e=\frac{{360}^0}{6}={60}^0$

Thus, we know that the sum of the polygon’s angle will measure

  $s=9({60}^0)={540}^0$

So, for any n sided polygon, we can say that

  $(n-2){180}^0={540}^0\to n=5$

Hence, the polygon is a pentagon