Question

the sum of the interior angle measures of a convex polygon is 2520°. how many sides does it have?
number of sides =

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 \(S = 2520^{\circ}\), we have \(2520=(n - 2)\times180\).

Step3: Solve for \(n\)

First, divide both sides of the equation by \(180\): \(\frac{2520}{180}=n - 2\).
Since \(\frac{2520}{180}=14\), the equation becomes \(14=n - 2\).
Then, add \(2\) to both sides: \(n=14 + 2\).

Answer:

\(16\)