Chapter 12.3, Problem 47E

To determine

To find :thesum of the measures of the interior angles of the gazebo base which is hexagon.

Answer to Problem 47E

the sum of the measures of the interior angles of the gazebo base which is hexagon is ${720}^{\circ }$ .

Explanation of Solution

Given : the polygonprovided in the question,

Base shape is hexagon.

Formula used:

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

Calculation: to find the sum of the measures of the interior angles of the gazebo base, substitute n by 6 in the formula because its shape is hexagon and hexagon has 6 sides.

  $\begin{array}{l}\left(n-2\right)·{180}^{\circ }\\ \left(6-2\right)·{180}^{\circ }\text{ [substitute n by 6]}\\ 4·{180}^{\circ }\text{ [subtract]}\\ {720}^{\circ }\text{ [multiply]}\end{array}$

Thus ,the sum of the measures of the interior angles of the gazebo base which is hexagon is ${720}^{\circ }$ .