Question

which polygon has an interior angle sum of 1080°?

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 of the polygon.

Step2: Set up the equation and solve for \(n\)

We are given that \(S = 1080^{\circ}\). So, \((n-2)\times180^{\circ}=1080^{\circ}\).
Divide both sides by \(180^{\circ}\): \(n - 2=\frac{1080^{\circ}}{180^{\circ}}=6\).
Then add \(2\) to both sides: \(n=6 + 2=8\).

A polygon with \(n = 8\) sides is an octagon.

Answer:

The polygon with \(8\) sides (octagon) has an interior - angle sum of \(1080^{\circ}\).