Question

what is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 120°?
a. 900°
b. 180°
c. 720°
d. 1080°
e. 540°
f. 360°

Explanation:

Step1: Find the number of sides

The sum of exterior angles of any polygon is 360°. Given each exterior angle is 120°. Let the number of sides be $n$. Then $n=\frac{360}{120}=3$.

Step2: Use interior - angle sum formula

The formula for the sum of interior angles of a polygon is $(n - 2)\times180^{\circ}$. Substitute $n = 3$ into the formula: $(3 - 2)\times180^{\circ}=180^{\circ}$.

Answer:

B. 180°