Chapter 12, Problem 17CR

To determine

To find: The number of sides of an equiangular polygon if each interior angle is 170.

Answer to Problem 17CR

The number of sides of an equiangular polygon is 36.

Explanation of Solution

Given Information:

In an equiangular polygon,

Measure of an interior angle $\left(a\right)={170}^{\text{o}}$

Formula used:

Measure of each interior angle $\left(a\right)=\frac{\left(n-2\right)}{n}\times {180}^{\text{o}}$

  $"a"$ is the interior angle of a regular polygon

  $"n"$ is the number of sides

Calculation:

In a regular polygon,

Measure of each interior angle $\left(a\right)=\frac{\left(n-2\right)}{n}\times {180}^{\text{o}}$

As $a={170}^{\text{o}}$

  $\begin{array}{l}\therefore {170}^{\text{o}}=\frac{\left(n-2\right)}{n}\times {180}^{\text{o}}\\ \therefore 17n=\left(n-2\right)18\\ \therefore 17n=18n-36\\ \therefore n=36\end{array}$

Hence, the number of sides of an equiangular polygon is 36.