Chapter 11.5, Problem 4CYU

To determine

To Find: The number of sides of a polygon.

Answer to Problem 4CYU

The number of sides of polygon is 12.

Explanation of Solution

Given information:

The sum of measure of angles of polygon is ${1800}^{°}$

Concept and Formula Used:

Sum of measure of angle of polygon is $=\left(n-2\right){180}^{°}$

Calculation:

The sum of measure of a polygon is $=\left(n-2\right){180}^{°}$

The sum of measure of angles of polygon is given i.e. ${1800}^{°}$

Therefore

Sum of angles of a pentagon is

  $\begin{array}{l}{1800}^{°}=\left(n-2\right)180°\\ \frac{1800}{180}=\left(n-2\right)\\ n-2=10\\ n=12\end{array}$

Conclusion:

The number of sides of polygon is 12.