Q55. - Algebra 1

Question

To find the measure of an interior angle of a regular polygon, you can use the formula $m=\frac{180(n-2)}{n}$, where m represents the measure of each angle and n represents the number of sides in the polygon. If $m=156$, how many sides does the polygon have? 

Step-by-Step Solution

Answer

The polygon has 15 sides.

Step 1. Substitute 156 for m .

$156=\frac{180(n-2)}{n}$

Step 2. Isolate the variable.

$\begin{array}{l}156=\frac{180(n-2)}{n}\\ 156n=180n-360\\ 360=180n-156n\\ 360=24n\end{array}$

Step 3. Divide both the sides by 24.

$\begin{array}{l}360=24n\\ \frac{24n}{24}=\frac{360}{24}\\ n=15\end{array}$

Hence, the polygon has 15 sides.