Question

which polygon has an interior angle sum of 900°?

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: Solve for \(n\)

Given \(S = 900^{\circ}\), we set up the equation \((n - 2)\times180^{\circ}=900^{\circ}\).
Divide both sides by \(180^{\circ}\): \(n - 2=\frac{900^{\circ}}{180^{\circ}} = 5\).
Then add 2 to both sides: \(n=5 + 2=7\). A polygon with \(n = 7\) sides is a heptagon.

Answer:

The polygon with an interior - angle sum of \(900^{\circ}\) is a heptagon.