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 of the polygon.

Step2: Substitute \(S = 900^{\circ}\) into the formula

We have \(900=(n - 2)\times180\).

Step3: Solve for \(n\)

Divide both sides of the equation by \(180\): \(\frac{900}{180}=n - 2\).
Since \(\frac{900}{180}=5\), then \(5=n - 2\).
Add \(2\) to both sides: \(n=5 + 2=7\).

Answer:

A heptagon (a polygon with \(7\) sides)