Answer :

GinnyAnswer
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.

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