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.
( \bigcirc ) 6 sides
( \bigcirc ) 7 sides
( \bigcirc ) 8 sides
( \bigcirc ) 9 sides

Explanation:

Step1: Substitute s into the formula

We know the formula \( s = 180(n - 2) \), and \( s = 1260 \). So we substitute \( s \) into the formula: \( 1260 = 180(n - 2) \)

Step2: Solve for n

First, divide both sides of the equation by 180: \( \frac{1260}{180}=n - 2 \)
Calculate \( \frac{1260}{180}=7 \), so \( 7 = n - 2 \)
Then, add 2 to both sides: \( n=7 + 2=9 \) Wait, no, wait, let's recalculate. Wait, \( 1260\div180 = 7 \), then \( n-2 = 7 \), so \( n=7 + 2=9 \)? But wait, let's check again. Wait, maybe I made a mistake. Wait, \( 180\times(9 - 2)=180\times7 = 1260 \). Oh right, so n is 9? But wait the options have 9 sides. Wait, but let's check the calculation again.

Wait, the formula is \( s = 180(n - 2) \), so we need to solve for n when s = 1260.

So:

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

Divide both sides by 180:

\( n - 2=\frac{1260}{180} \)

\( \frac{1260}{180}=7 \) (because 180*7=1260)

Then, \( n - 2 = 7 \)

Add 2 to both sides:

\( n=7 + 2=9 \)

So the number of sides is 9.

Answer:

D. 9 sides (assuming the options are A.6 sides, B.7 sides, C.8 sides, D.9 sides)