Question

Each interior angle of a regular polygon has measure 150. How many sides does the polygon have?

Short answer

The number of sides in the regular polygon having measure of each interior angles as 150 is 12.

Step-by-step solution

Step 1. Write the formula to find the measure of each interior angle for a regular polygon with n sides.

The formula to find the measure of each interior angle for a regular polygon with$n$ sides is $\frac{\left(n-2\right)\mathbf{180}}{n}$.

Step 2. Find the value of n having measure of each interior angle for a regular polygon as 150.

The measure of each interior angle for a regular polygon is 150.

Therefore, the value of$n$is given by:

$$\begin{gathered} 150=\frac{\left(n-2\right)180}{n} \\ 150n=\left(n-2\right)180 \\ 150n=180n-360 \\ 360=180n-150n \\ 360=30n \\ \frac{360}{30}=n \\ 12=n \end{gathered}$$

Therefore, the value of$n$ is 12.

Step 3. Write the conclusion.

Therefore, the number of sides in the regular polygon having measure of each interior angles as 150 is 12.