Question

how many sides does a polygon have if the sum of the interior angles is 4140°?

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 \(S = 4140^{\circ}\), we have \(4140=(n - 2)\times180\).

Step3: Solve for \(n\)

First, divide both sides by \(180\): \(\frac{4140}{180}=n - 2\).
Since \(\frac{4140}{180}=23\), then \(23=n - 2\).
Add \(2\) to both sides: \(n=23 + 2\).

Answer:

\(n = 25\)