Chapter 12.3, Problem 48E

To determine

To find :thesum of the measures of the interior angles of the stop sign which is octagon.

Answer to Problem 48E

the sum of the measures of the interior angles of the stop sign which is octagon is ${1080}^{\circ }$ .

Explanation of Solution

Given : consider, the polygonprovided in the question,

Stop sign shape octagon.

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 stop sign, substitute n by 8 in the formula because its shape is octagon and octagon has 8 sides.

  $\begin{array}{l}\left(n-2\right)·{180}^{\circ }\\ \left(8-2\right)·{180}^{\circ }\text{ [substitute n by 8]}\\ 6·{180}^{\circ }\text{ [subtract]}\\ {1080}^{\circ }\text{ [multiply]}\end{array}$

Thus ,the sum of the measures of the interior angles of the stop sign which is octagon is ${1080}^{\circ }$ .