Question

1. the sum of the interior angles of a polygon is 1620°. how many sides does the polygon have?

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \), where \( S \) is the sum of the interior angles and \( n \) is the number of sides.

Step2: Substitute the given sum into the formula and solve for \( n \)

We are given that \( S = 1620^{\circ} \). Substituting this into the formula:
\[
1620=(n - 2)\times180
\]
First, divide both sides of the equation by \( 180 \):
\[
\frac{1620}{180}=n - 2
\]
\( \frac{1620}{180}=9 \), so:
\[
9=n - 2
\]
Then, add \( 2 \) to both sides of the equation:
\[
n=9 + 2
\]
\[
n = 11
\]

Answer:

The polygon has 11 sides.