Chapter 12.3, Problem 12E

To determine

To find : The measure of an interior angle and the measure of an exterior angle for the regular triangle.

Answer to Problem 12E

The measure of an interior angle of regular triangle is ${60}^{\circ }$ and the measure of an exterior angle of a regular triangle is ${120}^{\circ }$ .

Explanation of Solution

Given information : Here, the polygon is regular triangle.

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

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. $n=3$

Therefore, the measure of an interior angle of regular triangle is

  $\begin{array}{l}\frac{\left(3-2\right)\times {180}^{\circ }}{3}\\ \Rightarrow \frac{1\times {180}^{\circ }}{3}\\ \Rightarrow \frac{{180}^{\circ }}{3}\\ \Rightarrow {60}^{\circ }\end{array}$

The measure of an exterior angle of a regular triangle is

  $\begin{array}{l}{180}^{\circ }-\frac{\left(3-2\right)\times {180}^{\circ }}{3}\\ \Rightarrow {180}^{\circ }-\frac{1\times {180}^{\circ }}{3}\\ \Rightarrow {180}^{\circ }-\frac{{180}^{\circ }}{3}\\ \Rightarrow {180}^{\circ }-{60}^{\circ }\\ \Rightarrow {120}^{\circ }\end{array}$