Chapter 12, Problem 5CST

To determine

To find: The sum of the measures of the interior angles of a convex octagon.

Answer to Problem 5CST

The sum of the measure of the interior angles of a convex octagon is ${1080}^{\circ }$ .

Explanation of Solution

Given information: A convex octagon.

Calculation: Since, To find the sum of the interior angle of any polygon, the formula is $=\left(\text{n-2}\right)\times {180}^{\circ }$ , Where, $n$ is the number of sides of the polygon.

The number of sides of an octagon is $8$ .

Therefore, The sum of the measure of the interior angles of a convex octagon is,

  $\begin{array}{l}=\left(\text{n-2}\right)\times {180}^{\circ }\\ =\left(8-2\right)\times {180}^{\circ }\\ =6\times {180}^{\circ }\\ ={1080}^{\circ }\end{array}$

Hence, The sum of the measure of the interior angles of a convex octagon is ${1080}^{\circ }$ .