Chapter 12.3, Problem 16E

To determine

To find :themeasure of an interior angle and an exterior angle for the regular $10-gon$ .

Answer to Problem 16E

The measure of an interior angle is ${144}^{\circ }$ and an exterior angle is ${36}^{\circ }$ for the regular $10-gon$ .

Explanation of Solution

Given information : the polygon provided in the question,

  $10-gon$ .

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 $10-gon$

  $n=10$ , so substitute the n by 10 in the formula, then subtract and multiply and then divide.

the measure of an interior angle of a regular $10-gon$ = $\begin{array}{l}\frac{\left(10-2\right)·{180}^{\circ }}{10}\text{ [substitute n by 10]}\\ \frac{8·{180}^{\circ }}{10}\text{ [subtract]}\\ {144}^{\circ }\text{ [multiply and divide]}\end{array}$ .

The measure of an exterior angle of a regular $10-gon$ = $\begin{array}{l}\frac{{360}^{\circ }}{10}\\ {36}^{\circ }\text{ [divide]}\end{array}$

Hence, The measure of an interior angle is ${144}^{\circ }$ and an exterior angle is ${36}^{\circ }$ for the regular $10-gon$ .