Question

which polygon has 720° as the sum of the measures of its interior angles?

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 of the polygon.

Step2: Solve for \(n\) when \(S = 720^{\circ}\)

Set up the equation \(720=(n - 2)\times180\).
Divide both sides by \(180\): \(\frac{720}{180}=n - 2\).
Since \(\frac{720}{180}=4\), then \(4=n - 2\).
Add \(2\) to both sides: \(n=4 + 2=6\).

Step3: Identify the polygon with \(n = 6\) sides

A polygon with \(6\) sides is a hexagon.

Answer:

C.