Question

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s=180(n−2), where n is the number of sides.

Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°? Round to the nearest whole number.

6 sides
7 sides
8 sides
9 sides

Answer 1

To find the number of sides (\( n \)) in a polygon given the sum of its interior angles (\( s \)), you can use the formula:

\[
s = 180(n - 2)
\]

Given that \( s = 1260^\circ \), we can set up the equation:

\[
1260 = 180(n - 2)
\]

Now, divide both sides by 180 to solve for \( n - 2 \):

\[
\frac{1260}{180} = n - 2
\]

Calculating the left side:

\[
7 = n - 2
\]

Now, add 2 to both sides:

\[
n = 7 + 2
\]
\[
n = 9
\]

Thus, the polygon has **9 sides**.

So, the answer is **9 sides**.