Chapter 6.2, Problem 52SPR

To determine

The number of sides in the polygon.

Answer to Problem 52SPR

The polygon has 11 sides.

Explanation of Solution

Given:

The measure of an interior angle of a regular polygon is 147.3.

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 $147.3n.$

So, put the value in the formula:

  $\begin{array}{l}Sum=\left(n-2\right)180\\ 147.3n=\left(n-2\right)180\\ 147.3n=180n-360\\ 360=32.7n\\ n=\frac{360}{32.7}\\ n=11\end{array}$

The polygon has 11 sides.