Question

if the sum of interior angle measures of a polygon is 540°, how many sides does the polygon have? a. 5 b. 4 c. 7 d. 6

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 $S = 540^{\circ}$. Substitute $S$ into the formula: $540=(n - 2)\times180$.

Step3: Solve for $n$

First, divide both sides of the equation by $180$: $\frac{540}{180}=n - 2$. Since $\frac{540}{180}=3$, the equation becomes $3=n - 2$.
Then, add $2$ to both sides of the equation: $n=3 + 2$. So, $n = 5$.

Answer:

A. 5