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^circ )? round to the nearest whole number.
options: 8 sides, 6 sides, 9 sides, 7 sides

Explanation:

Step1: Start with the given formula

We know the formula for the sum of interior angles of an \( n \)-sided polygon is \( s = 180(n - 2) \), and we are given that \( s = 1260 \). So we substitute \( s \) with 1260 in the formula:
\[ 1260 = 180(n - 2) \]

Step2: Solve for \( n \)

First, divide both sides of the equation by 180:
\[ \frac{1260}{180} = n - 2 \]
\[ 7 = n - 2 \]
Then, add 2 to both sides to isolate \( n \):
\[ n = 7 + 2 \]
\[ n = 9 \]
Wait, no, wait. Wait, \( 1260\div180 = 7 \), so \( 7=n - 2 \), then \( n=7 + 2=9 \)? But wait, let's check again. Wait, the options have 9 sides as an option. Wait, but let's re - calculate. Wait, \( s = 180(n - 2) \), so \( n=\frac{s}{180}+2 \). If \( s = 1260 \), then \( \frac{1260}{180}=7 \), so \( n = 7+2 = 9 \). But wait, the options also have 7 sides. Wait, maybe I made a mistake. Wait, no, let's check with \( n = 7 \). If \( n = 7 \), then \( s=180\times(7 - 2)=180\times5 = 900
eq1260 \). If \( n = 9 \), \( s=180\times(9 - 2)=180\times7 = 1260 \). So the correct answer is 9 sides.

Answer:

9 sides (corresponding to the option "9 sides")