Question

if the sum of interior angle measures of a polygon is 720°, how many sides does the polygon have?
a. 6
b. 8
c. 9
d. 7

Explanation:

Step1: Recall the formula

The formula for the sum of interior - angles of a polygon is $S=(n - 2)\times180^{\circ}$, where $S$ is the sum of interior - angles and $n$ is the number of sides.

Step2: Substitute the given sum

We are given that $S = 720^{\circ}$, so we set up the equation $720=(n - 2)\times180$.

Step3: Solve for $n$

First, divide both sides of the equation by 180: $\frac{720}{180}=n - 2$. Since $\frac{720}{180}=4$, the equation becomes $4=n - 2$. Then, add 2 to both sides: $n=4 + 2=6$.

Answer:

A. 6