Question

applying the polygon interior angle sum theorem
which polygon has an interior angle sum of 1260°?

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 \(S = 1260^{\circ}\) into the formula

We have \(1260=(n - 2)\times180\).

Step3: Solve for \(n\)

Divide both sides by \(180\): \(\frac{1260}{180}=n - 2\).
Since \(\frac{1260}{180}=7\), then \(7=n - 2\).
Add \(2\) to both sides: \(n=7 + 2=9\).

Answer:

A non - agon (a polygon with 9 sides) has an interior angle sum of \(1260^{\circ}\).