Chapter 12.3, Problem 4C

To determine

To find : The exterior angle of the regular pentagon.

Answer to Problem 4C

The measure of an exterior angle of a regular triangle is ${72}^{\circ }$ .

Explanation of Solution

Given information : Here, the polygon is regular pentagon.

Formula used :

All exterior angles of a regular polygon are equal and the measure of an exterior angle of regular n-gon is ${180}^{\circ }-\frac{\left(n-2\right)\times {180}^{\circ }}{n}$

Calculation :

Here, polygon is regular triangle i.e. $n=5$

The measure of an exterior angle of a regular pentagon is ${72}^{\circ }$

  $\begin{array}{l}{180}^{\circ }-\frac{\left(5-2\right)\times {180}^{\circ }}{5}\\ \Rightarrow {180}^{\circ }-\frac{3\times {180}^{\circ }}{5}\\ \Rightarrow {180}^{\circ }-\frac{{540}^{\circ }}{5}\\ \Rightarrow {180}^{\circ }-{108}^{\circ }\\ \Rightarrow {72}^{\circ }\end{array}$

Therefore, the measure of an exterior angle of a regular triangle is ${72}^{\circ }$