Chapter 12.3, Problem 8E

To determine

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

Answer to Problem 8E

The sum of the measures of all interior angles of a convex pentagon is ${540}^{\circ }$ .

Explanation of Solution

Given information : Here, the polygon is convex pentagon.

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 pentagon i.e. $n=5$

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

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

The sum of the measures of all interior angles of a convex pentagon is ${540}^{\circ }$ .