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. 8 sides 9 sides 7 sides 6 sides

Explanation:

Step1: Substitute s into the formula

We know the formula for the sum of interior angles of a 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: \( \frac{1260}{180}=n - 2 \). Calculating \( \frac{1260}{180} \), we get 7. So the equation becomes \( 7 = n - 2 \). Then, add 2 to both sides to solve for \( n \): \( n = 7 + 2 = 9 \).

Answer:

B. 9 sides