Question

the sum of the interior angle measures of a convex polygon is 720°. 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 convex polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides and \(S\) is the sum of interior angles.

Step2: Substitute the given sum into the formula

Given \(S = 720^{\circ}\), we substitute into the formula: \(720=(n - 2)\times180\).

Step3: Solve for \(n\)

Divide both sides of the equation by \(180\): \(\frac{720}{180}=n - 2\).
Since \(\frac{720}{180}=4\), the equation becomes \(4=n - 2\).
Add \(2\) to both sides: \(n=4 + 2\).

Answer:

\(6\)