Chapter 12.3, Problem 1C

To determine

To find : The sum of the measure of the interior angles of the given $10$ -gon.

Answer to Problem 1C

The sum of the measures of all interior angles of a convex $10$ -gon is ${1440}^{\circ }$ .

Explanation of Solution

Given information : Here, the polygon is convex $10$ -gon.

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. $n=10$

Therefore, the sum of the all interior angle of a convex $10$ -gon is

  $\begin{array}{l}\left(n-2\right)\times {180}^{\circ }\\ \Rightarrow \left(10-2\right)\times {180}^{\circ }\\ \Rightarrow 8\times {180}^{\circ }\\ \Rightarrow {1440}^{\circ }\end{array}$

Therefore, the sum of the measures of all interior angles of a convex $10$ -gon is ${1440}^{\circ }$ .