Chapter 15, Problem 13CR

To determine

To Find: The total number of diagonals in a regular polygon.

Answer to Problem 13CR

  $135$

Explanation of Solution

Given:

Each interior angle of a regular polygon $=160$

Formula Used:

The sum of the measures of the exterior angles of a polygon is $=360$

  $d=\frac{n\left(n-3\right)}{2}$

Calculation:

  $\begin{array}{l}\text{Exterior angle}=180-160={20}^o\\ \text{⇒}{S}_e=360\\ \text{⇒}\frac{360}{20}=18\\ \text{⇒}d=\frac{18\left(18-3\right)}{2}=135\end{array}$

Conclusion:

Thus the required number of diagonals are $135$ .