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

1 answer

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.