Chapter 11.5, Problem 43STP

To determine

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

Answer to Problem 43STP

The measure of interior angle of 20-gon is ${162}^{°}$ .

Explanation of Solution

Given information:

The polygon has 20 sides.

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 polygon is $n=20$

Therefore

Sum of angles of a polygon is

  $\begin{array}{l}=\left(20-2\right){180}^{°}\\ \text{Sum}=18\times {180}^{°}\\ \text{Sum}={3240}^{°}\end{array}$

Total number of angles in a 20 sided polygon is 20.

The measure of each angle is

  $=\frac{{3240}^{°}}{20}={162}^{°}$

Conclusion:

The measure of interior angle of 20-gon is ${162}^{°}$ .