Chapter 8.1, Problem 62SPR

To determine

The type of polygon.

Answer to Problem 62SPR

Pentagon.

Explanation of Solution

Given:

Interior angle = 108 degrees.

Calculation:

The sum of interior angles of a n sided polygon is:

  $\left(n-2\right)\cdot 180$

The sum of the interior angle will be $108n$

The value of $n$ will be:

  $\begin{array}{l}\left(n-2\right)\cdot 180=108n\\ 180n-360=108n\\ 180n-108n=360\\ 72n=360\\ n=5\end{array}$

Hence, the polygon is a pentagon.