Question

question 32 of 33
if the sum of interior angle measures of a polygon is 720°, how many sides does the polygon have?
a. 4
b. 7
c. 6
d. 5

Explanation:

Step1: Recall polygon - interior - angle 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 into the formula

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:

C. 6