Chapter 3.5, Problem 16WE

To determine

Number of sides in polygon.

Answer to Problem 16WE

Number of sides in polygon is 12

Explanation of Solution

Given:

Sum of interior angle of polygon is 5 times of sum of exterior angle of polygon.

Sum of interior angle of polygon is given by, $\left(n-2\right)\times {180}^0$

Sum of exterior angle of polygon is equal to ${360}^0$

Now, according to question.

  $\begin{array}{l}\left(n-2\right)\times {180}^0=5\times {360}^0\\ n\times {180}^0-{360}^0={1800}^0\\ n\times {180}^0={2160}^0\\ n=\frac{{2160}^0}{{180}^0}\\ =12\end{array}$

Therefore, number of sides in polygon is 12