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 polygon with \( n \) sides, the measure of each interior angle \( I \) is given by \( I=\frac{(n - 2)\times180^{\circ}}{n} \). We know \( I = 150^{\circ} \), so we set up the equation \( 150=\frac{(n - 2)\times180}{n} \).

Step2: Solve the equation

Multiply both sides by \( n \): \( 150n=(n - 2)\times180 \)
Expand the right - hand side: \( 150n = 180n-360 \)
Subtract \( 150n \) from both sides: \( 0 = 180n-150n - 360 \)
Simplify: \( 0 = 30n-360 \)
Add 360 to both sides: \( 30n=360 \)
Divide both sides by 30: \( n=\frac{360}{30}=12 \)

Answer:

12