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.