Question

1. which polygon has an interior angle sum of 3960°? show work

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: Substitute \(S = 3960^{\circ}\) into the formula

We have \(3960=(n - 2)\times180\).

Step3: Solve for \(n\)

First, divide both sides of the equation by \(180\): \(\frac{3960}{180}=n - 2\).
Since \(\frac{3960}{180}=22\), then \(22=n - 2\).
Add \(2\) to both sides: \(n=22 + 2=24\).

Answer:

The polygon has \(24\) sides.