Chapter 12.3, Problem 4E

To determine

To find : The measure of an interior angle regular hexagon.

Answer to Problem 4E

The measure of an interior angle of regular hexagon is ${120}^{\circ }$

Explanation of Solution

Given information : Here, the polygon is regular hexagon.

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

Calculation :

Here, polygon is regular hexagon i.e. $n=6$

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

  $\begin{array}{l}\frac{\left(6-2\right)\times {180}^{\circ }}{6}\\ \Rightarrow \frac{4\times {180}^{\circ }}{6}\\ \Rightarrow \frac{{720}^{\circ }}{6}\\ \Rightarrow {120}^{\circ }\end{array}$

Therefore, the measure of an interior angle of regular hexagon is ${120}^{\circ }$