Chapter 12.3, Problem 10E

To determine

To find : The sum of the measure of the interior angles of the given hexagon.

Answer to Problem 10E

The sum of the measures of all interior angles of a convex hexagon is ${720}^{\circ }$ .

Explanation of Solution

Given information : Here, the polygon is convex hexagon.

Formula used : The sum of the measure of the all interior angles of a convex n-gon is $\left(n-2\right)\times {180}^{\circ }$

Calculation :

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

Therefore, the sum of the all interior angle of a convex hexagon is

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

The sum of the measures of all interior angles of a convex hexagon is ${720}^{\circ }$ .