Question

question 10 of 10
what is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 72°?
a. 180°
b. 1080°
c. 540°
d. 900°
e. 720°
f. 360°

Explanation:

Step1: Find the number of sides.

The sum of exterior angles of any polygon is $360^{\circ}$. If each exterior angle of a regular polygon is $72^{\circ}$, then the number of sides $n=\frac{360}{72}=5$.

Step2: Use the interior - angle sum formula.

The formula for the sum of interior angles of a polygon is $(n - 2)\times180^{\circ}$. Substituting $n = 5$ into the formula, we get $(5 - 2)\times180^{\circ}=3\times180^{\circ}=540^{\circ}$.

Answer:

C. $540^{\circ}$