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

We set \((n - 2)\times180^{\circ}=1080^{\circ}\).

Step3: Solve for \(n\)

Divide both sides of the equation by \(180^{\circ}\): \(\frac{(n - 2)\times180^{\circ}}{180^{\circ}}=\frac{1080^{\circ}}{180^{\circ}}\), which gives \(n - 2 = 6\). Then add \(2\) to both sides: \(n=6 + 2=8\). A polygon with \(n = 8\) sides is an octagon.

Answer:

The polygon with 8 vertices (the octagon - we assume the correct figure among the options is the one with 8 vertices as per the calculation of \(n = 8\) from \((n - 2)\times180=1080\))