Chapter 11.5, Problem 18PPS

To determine

To find the measure of an interior angle of an octagon.

Answer to Problem 18PPS

Interior angle of the octagon is ${135}^{\circ }$ .

Explanation of Solution

Given:

The dome in a state capitol building is octagonal.

Concept used:

The interior angle of a polygon with n sides is $\frac{\left(n-2\right)\times {180}^{\circ }}{n}$ .

Calculation:

Given that the dome in a state capitol building is octagonal, which mean that the number of sides is 8.

Therefore interior angle is,

  $\begin{array}{l}\frac{\left(n-2\right)\times {180}^{\circ }}{n}=\frac{\left(8-2\right)\times {180}^{\circ }}{8}\\ =\frac{6\times {180}^{\circ }}{8}\\ =\frac{{1080}^{\circ }}{8}\\ ={135}^{\circ }\end{array}$

Hence interior angle of an octagon is ${135}^{\circ }$ .