Question

the sum of the measures of the interior angles of a regular polygon is 2340 degrees. how many sides does the polygon have?

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

We know that \(S = 2340^{\circ}\), so we set up the equation \(2340=(n - 2)\times180\).

Step3: Solve for \(n\)

First, divide both sides of the equation by \(180\): \(\frac{2340}{180}=n - 2\).
Since \(\frac{2340}{180}=13\), then \(13=n - 2\).
Next, add \(2\) to both sides: \(n=13 + 2\).

Answer:

The polygon has \(15\) sides.