Question

question 3 of 25 if the sum of interior angle measures of a polygon is 1080°, how many sides does the polygon have? a. 9 b. 10 c. 7 d. 8

Explanation:

Step1: Recall the formula

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

Step2: Substitute the given sum

We are given that $S = 1080^{\circ}$. So, we set up the equation $1080=(n - 2)\times180$.

Step3: Solve for $n$

First, divide both sides of the equation by $180$: $\frac{1080}{180}=n - 2$. Since $\frac{1080}{180}=6$, the equation becomes $6=n - 2$. Then, add $2$ to both sides: $n=6 + 2=8$.

Answer:

D. 8