Question

1. if the sum of the measures of the interior angles of a polygon is 1980°, how many sides does the polygon have?

Explanation:

Step1: Recall the formula

The sum of the interior - angle measures of a polygon is given by the formula $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides of the polygon and $S$ is the sum of the interior - angle measures.

Step2: Substitute the given sum

We are given that $S = 1980^{\circ}$. So, we set up the equation $(n - 2)\times180^{\circ}=1980^{\circ}$.

Step3: Solve for $n$

First, divide both sides of the equation by $180^{\circ}$:
$n - 2=\frac{1980^{\circ}}{180^{\circ}}$.
Since $\frac{1980}{180}=11$, we have $n - 2 = 11$.
Then, add 2 to both sides of the equation: $n=11 + 2$.
So, $n = 13$.

Answer:

13