Chapter 11, Problem 15CR

To determine

To find: Measure of each interior angle of regular polygon.

Answer to Problem 15CR

Measure of each interior angle of given figure is ${135}^0$

Explanation of Solution

Given information:

From given figure

We can say that

  $n=8$

We know

Sum of measure of interior angles of a polygon is $\left(n-2\right){180}^0$

Given

  $n=8$

On substituting values

We get

  $\Rightarrow$ Sum of measure of interior angles of a polygon is $\left(8-2\right){180}^0$

  $\Rightarrow$ Sum of measure of interior angles of a polygon is $\left(6\right){180}^0$

  $\Rightarrow$ Sum of measure of interior angles of a polygon is ${1080}^0$

As there are eight sides

We need to divide the Sum by $8$ to find the measure of one angle.

Measure of each interior angle $=\frac{{1080}^0}{8}$

  $\Rightarrow$ Measure of each interior angle $={135}^0$

Therefore,

Measure of each interior angle of given figure is ${135}^0$