Chapter 11.5, Problem 41STP

To determine

To find the number of sides of the polygon.

Answer to Problem 41STP

Polygon has 14 sides & option G is correct.

Explanation of Solution

Given:

The sum of the measures of the interior angles of a polygon is ${2160}^{\circ }$ .

Concept used:

The sum of all the interior angles of a polygon with n sides is $\left(n-2\right)\times {180}^{\circ }$ .

Calculation:

Let the number of sides of the polygon be n.

Now given that the sum of the interior angles of the polygon is ${2160}^{\circ }$ .

Therefore,

  $\begin{array}{l}\left(n-2\right)\times {180}^{\circ }={2160}^{\circ }\\ \Rightarrow n-2=\frac{{2160}^{\circ }}{{180}^{\circ }}\\ \Rightarrow n-2=12\\ \Rightarrow n=14\end{array}$

Therefore polygon has 14 sides.

Hence option G is correct.