Chapter 11.5, Problem 3GP

To determine

To find the measure of an interior angle of one of the pentagonal panels in soccer ball.

Answer to Problem 3GP

Interior angle of the pentagonal panel is ${108}^{\circ }$ .

Explanation of Solution

Given:

Pentagonal panel of a soccer ball.

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 panel is in the shape of a pentagon, which means that the number of sides is 5.

Therefore interior angle is,

  $\begin{array}{l}\frac{\left(n-2\right)\times {180}^{\circ }}{n}=\frac{\left(5-2\right)\times {180}^{\circ }}{5}\\ =\frac{3\times {180}^{\circ }}{5}\\ =\frac{{540}^{\circ }}{5}\\ ={108}^{\circ }\end{array}$

Hence interior angle of an octagon is ${108}^{\circ }$ .