Question

the sum of the interior angle measures of a convex polygon is 900°. how many sides does it have?
number of sides =

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 \(S\) is the sum of interior angles and \(n\) is the number of sides.

Step2: Substitute the given sum into the formula

Given \(S = 900^{\circ}\), we substitute into the formula: \(900=(n - 2)\times180\).

Step3: Solve for \(n\)

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

Answer:

\(7\)