Chapter 6, Problem 4STP

To determine

The measure of an interior angle of a regular pentagon.

Answer to Problem 4STP

Option G. 108 is correct.

Explanation of Solution

Given:

The polygon is a pentagon.

Calculation:

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

  $\left(n-2\right)180$

The sides in a pentagon are 5.

So, put the value in the formula:

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

The sum of the measures of interior angles of a pentagon is 540.

As, the given figure is a pentagon, all interior angles are congruent.

Calculating the measure of one interior angle;

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

Thus, Option G. 108 is correct.