Question

how many sides does a polygon have if the sum of the interior angles is 1800°?
answer attempt 1 out of 2

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 \( S = 1800^{\circ} \). Substitute this into the formula:
\[
1800=(n - 2)\times180
\]
First, divide both sides of the equation by \( 180 \):
\[
\frac{1800}{180}=n - 2
\]
Simplify the left - hand side: \( 10=n - 2 \)
Then, add 2 to both sides of the equation to solve for \( n \):
\[
n=10 + 2
\]
\[
n = 12
\]

Answer:

The polygon has 12 sides.