Question
The interior angle sum of a convex polygon is 1,980°. How many sides does the polygon have?
Answers
GPT-4o mini
To find the number of sides \( n \) of a convex polygon based on its interior angle sum, we can use the formula for the interior angle sum:
\[
S = (n - 2) \times 180^\circ
\]
where \( S \) is the sum of the interior angles and \( n \) is the number of sides.
Given that the sum of the interior angles \( S = 1980^\circ \), we can set up the equation:
\[
1980 = (n - 2) \times 180
\]
Next, we solve for \( n \). First, divide both sides by 180:
\[
\frac{1980}{180} = n - 2
\]
Calculating the left side:
\[
11 = n - 2
\]
Now, add 2 to both sides to solve for \( n \):
\[
n = 11 + 2 = 13
\]
Thus, the polygon has
\[
\boxed{13}
\]
sides.
\[
S = (n - 2) \times 180^\circ
\]
where \( S \) is the sum of the interior angles and \( n \) is the number of sides.
Given that the sum of the interior angles \( S = 1980^\circ \), we can set up the equation:
\[
1980 = (n - 2) \times 180
\]
Next, we solve for \( n \). First, divide both sides by 180:
\[
\frac{1980}{180} = n - 2
\]
Calculating the left side:
\[
11 = n - 2
\]
Now, add 2 to both sides to solve for \( n \):
\[
n = 11 + 2 = 13
\]
Thus, the polygon has
\[
\boxed{13}
\]
sides.