To determine how many sides a polygon has based on the sum of its interior angles, we can use the formula:
[tex]\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\][/tex]
where [tex]\( n \)[/tex] represents the number of sides of the polygon. We are given that the sum of the interior angles is 720°. Let's find [tex]\( n \)[/tex] by solving the equation:
1. Set up the equation using the given sum of interior angles:
[tex]\[
720 = (n - 2) \times 180
\][/tex]
2. Solve for [tex]\( n \)[/tex]:
- First, divide both sides of the equation by 180 to isolate [tex]\( n - 2 \)[/tex]:
[tex]\[
\frac{720}{180} = n - 2
\][/tex]
- Calculate the left side:
[tex]\[
4 = n - 2
\][/tex]
- Add 2 to both sides to solve for [tex]\( n \)[/tex]:
[tex]\[
4 + 2 = n
\][/tex]
[tex]\[
n = 6
\][/tex]
Therefore, the polygon has 6 sides.
The correct answer is:
○ A. 6
