Chapter 12.3, Problem 3E

To determine

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

Answer to Problem 3E

The sum of the measures of all interior angles of a convex heptagon is ${900}^{\circ }$ .

Explanation of Solution

Given information : Here, the polygon is convex heptagon.

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 heptagon i.e. $n=7$

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

  $\begin{array}{l}\left(n-2\right)\times {180}^{\circ }\\ \Rightarrow \left(7-2\right)\times {180}^{\circ }\\ \Rightarrow 5\times {180}^{\circ }\\ \Rightarrow {900}^{\circ }\end{array}$

Therefore, the sum of the measures of all interior angles of a convex heptagon is ${900}^{\circ }$ .