Question

question 5 of 25
if the sum of interior angle measures of a polygon is 900°, how many sides does the polygon have?
a. 8
b. 10
c. 7
d. 9

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 and $S$ is the sum of interior angles.

Step2: Substitute the given sum

We are given that $S = 900^{\circ}$. So, we set up the equation $900=(n - 2)\times180$.

Step3: Solve for $n$

First, divide both sides of the equation by 180: $\frac{900}{180}=n - 2$. Since $\frac{900}{180}=5$, the equation becomes $5=n - 2$. Then, add 2 to both sides: $n=5 + 2=7$.

Answer:

C. 7