Question

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

Explanation:

Step1: Recall the formula for the sum of interior angles

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

Step2: Substitute the given sum into the formula

Given \(S = 720^{\circ}\), we have \(720=(n - 2)\times180\).

Step3: Solve for \(n\)

Divide both sides by \(180\): \(\frac{720}{180}=n - 2\).
\(4=n - 2\).
Add \(2\) to both sides: \(n=4 + 2=6\).

Answer:

D. 6