Chapter 6.2, Problem 55SPR

To determine

The number of sides in the polygon.

Answer to Problem 55SPR

The polygon has 100 sides.

Explanation of Solution

Given:

The measure of an interior angle of a regular polygon is 176.4.

Calculation:

The sum of the measures of interior angles of an n-sided polygon is:

  $\left(n-2\right)180$

Let n be the number of sides in the polygon. As all the angles of a regular polygon are congruent, the sum of interior angle measure is $176.4n.$

So, put the value in the formula:

  $\begin{array}{l}Sum=\left(n-2\right)180\\ 176.4n=\left(n-2\right)180\\ 176.4n=180n-360\\ 360=3.6n\\ n=\frac{360}{3.6}\\ n=100\end{array}$

The polygon has 100 sides.