Question

how many sides does a polygon have if the sum of the interior angles is $1800^{circ}$?

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 \( S = 1800^{\circ} \). Substituting into the formula \( 1800=(n - 2)\times180 \).
First, divide both sides of the equation by \( 180 \):
\( \frac{1800}{180}=n - 2 \)
\( 10=n - 2 \)
Then, add \( 2 \) to both sides of the equation:
\( n=10 + 2 \)
\( n = 12 \)

Answer:

The polygon has 12 sides.