Question

how many sides does a polygon have if the sum of the interior angles is 3780°?

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 know that \( S = 3780^{\circ} \). Substitute this into the formula:

$$ 3780=(n - 2)\times180 $$

First, divide both sides of the equation by \( 180 \):

$$ \frac{3780}{180}=n - 2 $$

Calculate \( \frac{3780}{180}=21 \), so we have:

$$ 21=n - 2 $$

Then, add \( 2 \) to both sides of the equation to solve for \( n \):

$$ n=21 + 2=23 $$

Answer:

The polygon has 23 sides.