Question

the sum of the measures of the interior angles of a convex polygon is ∠1,980. how many sides does the polygon have? a convex polygon has choose... sides when the interior angle sum is ∠1980°. choose... 13 17 15 19

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 convex polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \), where \( S \) is the sum of the interior angles.

Step2: Substitute the given sum into the formula and solve for \( n \)

We know that \( S = 1980^{\circ} \). Substitute this into the formula:

$$ 1980=(n - 2)\times180 $$

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

$$ \frac{1980}{180}=n - 2 $$

Calculate \( \frac{1980}{180}=11 \), so we have:

$$ 11=n - 2 $$

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

$$ n=11 + 2=13 $$

Answer:

13