Chapter 11.5, Problem 26PPS

To determine

To identify the polygon.

Answer to Problem 26PPS

The polygon is a 30-gon.

Explanation of Solution

Given:

The sum of the interior angles of the polygon is ${5040}^{\circ }$ .

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 required polygon have n sides.

Now given that the sum of the interior angles of the polygon is ${5040}^{\circ }$ .

Therefore,

  $\begin{array}{l}\left(n-2\right)\times {180}^{\circ }={5040}^{\circ }\\ \Rightarrow n-2=\frac{{5040}^{\circ }}{{180}^{\circ }}\\ \Rightarrow n-2=28\\ \Rightarrow n=30\end{array}$

Hence the polygon is a 30-gon.