Chapter 6.1, Problem 22PPS

To determine

The measure of each interior angle of each regular polygon.

Answer to Problem 22PPS

The measure of each interior angle of the given polygon is 108.

Explanation of Solution

Given:

The given polygon is pentagon.

Calculation:

The sum of the measures of interior angles of an n-sided polygon is:

  $\left(n-2\right)180$

Pentagon has 5 sides.

So, put the value in the formula:

  $\begin{array}{l}Sum=\left(n-2\right)180\\ Sum=\left(5-2\right)180\\ Sum=\left(3\right)180\\ Sum=540\end{array}$

As the given polygon is a regular 5-gon, the interior angles are congruent.

Calculating the measure of one interior angle:

  $\begin{array}{l}\frac{\text{Sum of interior angle measures}}{\text{Number of congruent angles}}=\frac{540}{5}\\ \text{ =108}\end{array}$

Therefore, the measure of each interior angle of the given polygon is 108.