Chapter 12.3, Problem 15E

To determine

To find :themeasure of an interior angle and an exterior angle for the regular pentagon.

Answer to Problem 15E

The measure of an interior angle is ${108}^{\circ }$ and an exterior angle is ${72}^{\circ }$ for the regular pentagon.

Explanation of Solution

Given information : the polygon provided in the question,

Pentagon.

Formula used: the measure of an interior angle of a regular n -gon is $\frac{\left(n-2\right)·{180}^{\circ }}{n}$ .

Each exterior angle for a regular n-gon has measure equal to 360/n degrees.

Calculation: for pentagon $n=5$ , so substitute the n by 5 in the formula, then subtract and then multiply and divide.

the measure of an interior angle of a regular pentagon = $\begin{array}{l}\frac{\left(5-2\right)·{180}^{\circ }}{5}\text{ [substitute n by 5]}\\ \frac{3·{180}^{\circ }}{5}\text{ [subtract]}\\ {108}^{\circ }\text{ [multiply, divide]}\end{array}$ .

The measure of an exterior angle of a regular pentagon = $\begin{array}{l}\frac{{360}^{\circ }}{5}\\ {72}^{\circ }\text{ [divide]}\end{array}$

Hence, The measure of an interior angle is ${108}^{\circ }$ and an exterior angle is ${72}^{\circ }$ for the regular pentagon .