Chapter 11.3, Problem 27IP

To determine

To identify the polygon by the given sum of the interior angle measures.

Answer to Problem 27IP

A regular 30-gon

Explanation of Solution

Given:

Sum of the interior angles: ${5040}^0$

Formula used:

Sum of the interior angles of a polygon: ${180}^0\times \left(n-2\right)$ where $n$ is the number of sides of the given polygon.

Calculation:

Let $n$ be the number of sides of the given polygon.

Now according to the formula of sum of interior angles of a polygon,

  $\Rightarrow {180}^0\times \left(n-2\right)$

As the sum is given,

  $\Rightarrow {180}^0\times \left(n-2\right)={5040}^0$

Now solving for n,

  $\Rightarrow n-2=\frac{{5040}^0}{{180}^0}$

  $\Rightarrow n-2=28$

  $\Rightarrow n=28+2$

  $\Rightarrow n=30$

Conclusion:

Therefore, the given polygon is a regular 30-gon.