Question

the measure of each interior angle of a regular polygon is 150°. find the number of sides.
number of sides =

Explanation:

Step1: Recall interior angle formula

For a regular $n$-sided polygon, each interior angle is $\frac{(n-2)\times180^\circ}{n}$.

Step2: Set up equation with given angle

$$150^\circ = \frac{(n-2)\times180^\circ}{n}$$

Step3: Solve for $n$ (eliminate degrees)

$$150n = 180(n-2)$$
$$150n = 180n - 360$$
$$360 = 180n - 150n$$
$$360 = 30n$$
$$n = \frac{360}{30}$$

Answer:

12