Chapter 7.4, Problem 12PSB

To determine

The name of the polygon is to be found

Answer to Problem 12PSB

The name of the polygon is Nonagon

Explanation of Solution

Given information : The following statement has been given

The ratio of the measure of an interior angle to the measure of an exterior angle is $7:2$

We know that the ratio of the interior angle to the exterior angle will be

  $\frac{\frac{(n-2){180}^0}{n}}{\frac{{360}^0}{n}}=\frac{7}{2}$

Hence, on solving for n , we get

  $n=9$

Thus, the polygon is a nonagon