Question

find the sum of the interior angle measures of the polygon. (see example 1.)

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: Determine \(n\) for each polygon

• For the first polygon (hexagon):

\(n = 6\).
Substitute \(n = 6\) into the formula: \(S=(6 - 2)\times180^{\circ}=4\times180^{\circ}=720^{\circ}\).

• For the second polygon (quadrilateral):

\(n = 4\).
Substitute \(n = 4\) into the formula: \(S=(4 - 2)\times180^{\circ}=2\times180^{\circ}=360^{\circ}\).

• For the third polygon (nonagon):

\(n = 9\).
Substitute \(n = 9\) into the formula: \(S=(9 - 2)\times180^{\circ}=7\times180^{\circ}=1260^{\circ}\).

Answer:

1. \(720^{\circ}\)
2. \(360^{\circ}\)
3. \(1260^{\circ}\)