Chapter 11.6, Problem 44SR

To determine

To Find: The measure of an interior angle of a pentagon.

Answer to Problem 44SR

The measure of each interior angle of pentagon is ${108}^{°}$ .

Explanation of Solution

Given information:

The polygon is pentagon.

Concept and Formula Used:

Sum of measure of angle of polygon is $=\left(n-2\right){180}^{°}$

Calculation:

The sum of measure of a polygon is $=\left(n-2\right){180}^{°}$

The number of sides in a pentagon is $n=5$

Therefore

Sum of angles of a pentagon is

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

Total number of angles in pentagon is 5 and all are equal.

Measure of each angle of a pentagon $=\frac{540}{5}={108}^{°}$

Conclusion:

The measure of each interior angle of pentagon is ${108}^{°}$ .