To determine the number of sides a polygon has if the sum of its interior angles is 1980°, we'll follow a clear step-by-step approach:
1. Understand the Formula:
The sum of the interior angles of a polygon with [tex]\( n \)[/tex] sides is given by the formula:
[tex]\[
\text{Sum of interior angles} = (n - 2) \times 180°
\][/tex]
Here, [tex]\( n \)[/tex] represents the number of sides.
2. Set Up the Equation:
We know the sum of the interior angles is 1980°. Therefore, we can set up the equation as:
[tex]\[
(n - 2) \times 180° = 1980°
\][/tex]
3. Solve for [tex]\( n \)[/tex]:
To find [tex]\( n \)[/tex], we first isolate the term [tex]\((n - 2)\)[/tex]:
[tex]\[
n - 2 = \frac{1980°}{180°}
\][/tex]
Now, calculate the division:
[tex]\[
n - 2 = 11
\][/tex]
Finally, add 2 to both sides to solve for [tex]\( n \)[/tex]:
[tex]\[
n = 11 + 2
\][/tex]
[tex]\[
n = 13
\][/tex]
4. Number of Sides:
Thus, the polygon has 13 sides.
5. Naming the Polygon:
A polygon with 13 sides is called a "tridecagon" or, more commonly, a "13-gon".
Therefore, a polygon with the sum of the interior angles equal to 1980° is a polygon with 13 sides, and it is named a tridecagon or a 13-gon.
