Question
The sum of the angle measures of a polygon with \( n \) sides is 720 . Find \( n \).
Ask by Boone Burgess. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( n = 6 \)
Solution
To find the number of sides \( n \) of a polygon given that the sum of its interior angles is 720 degrees, we can use the formula for the sum of the interior angles of an \( n \)-sided polygon:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
Given that the sum is 720 degrees:
\[
(n - 2) \times 180 = 720
\]
Now, solve for \( n \):
\[
n - 2 = \frac{720}{180}
\]
\[
n - 2 = 4
\]
\[
n = 4 + 2
\]
\[
n = 6
\]
**Answer:** 6
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the number of sides \( n \) in a polygon given that the sum of its interior angle measures is 720 degrees, we can use the formula for the sum of the interior angles of a polygon, which is: \[ \text{Sum of interior angles} = (n - 2) \times 180 \] Setting this equal to 720 gives us: \[ (n - 2) \times 180 = 720 \] Now, we can solve for \( n \): 1. Divide both sides by 180: \[ n - 2 = \frac{720}{180} = 4 \] 2. Add 2 to both sides: \[ n = 4 + 2 = 6 \] So, the polygon has \( n = 6 \) sides, making it a hexagon!
