Question

1. a). a convex polygon has 1440° as the sum of its interior angles. find the number sides of the polygon
2. find the sum of interior angles of a convex polygon with 13 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.

Step2: Solve for \(n\) in the first problem

Given \(S = 1440^{\circ}\), we set up the equation \((n-2)\times180=1440\).
Divide both sides by \(180\): \(n - 2=\frac{1440}{180}=8\).
Then add \(2\) to both sides: \(n=8 + 2=10\).

Step3: Solve for \(S\) in the second problem

Given \(n = 13\), use the formula \(S=(n - 2)\times180^{\circ}\).
Substitute \(n = 13\) into the formula: \(S=(13-2)\times180^{\circ}=11\times180^{\circ}=1980^{\circ}\).

Answer:

1. The polygon has \(10\) sides.
2. The sum of interior angles is \(1980^{\circ}\).