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 \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides.

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

We set \((n - 2)\times180^{\circ}=1080^{\circ}\).
Divide both sides by \(180^{\circ}\): \(\frac{(n - 2)\times180^{\circ}}{180^{\circ}}=\frac{1080^{\circ}}{180^{\circ}}\), so \(n - 2 = 6\).
Add \(2\) to both sides: \(n=6 + 2=8\).

Answer:

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