Question

the sum of the measures of the interior angles of a polygon is 2880°. how many sides does the polygon have?
14
16
18
20

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 \(S\) is the sum of interior angles and \(n\) is the number of sides.

Step2: Substitute the given sum into the formula

Given \(S = 2880^{\circ}\), we have the equation \(2880=(n - 2)\times180\).

Step3: Solve for \(n\)

First, divide both sides of the equation by \(180\): \(\frac{2880}{180}=n - 2\).
Since \(\frac{2880}{180}=16\), the equation becomes \(16=n - 2\).
Then, add \(2\) to both sides: \(n=16 + 2\).

Answer:

18