Chapter 11, Problem 14CR

To determine

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

Answer to Problem 14CR

Measure of each interior angle of a 18-gon is ${160}^0$

Explanation of Solution

Given information:

18-gon it means

  $n=18$

We know

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

Given

  $n=18$

On substituting values

We get

  $\Rightarrow$ Sum of measure of interior angles of a polygon is $\left(18-2\right){180}^0$

  $\Rightarrow$ Sum of measure of interior angles of a polygon is $\left(16\right){180}^0$

  $\Rightarrow$ Sum of measure of interior angles of a polygon is ${2880}^0$

As there are eighteen sides

We need to divide the Sum by $18$ to find the measure of one angle.

Measure of each interior angle $=\frac{{2880}^0}{18}$

  $\Rightarrow$ Measure of each interior angle $={160}^0$

Therefore,

Measure of each interior angle of a18-gon is ${160}^0$