volume_mute
Find the Number of Sides Given the Angle Sum
publish date: 2026/05/16 08:22:29.500243 UTC
volume_mute
The sum of the angle measures of a polygon is 1,080°. How many sides does the polygon have?
Correct Answer
8 sides
Explanation
Substitute \(S = 1{,}080°\) and solve for \(n\):
\[1{,}080 = (n-2) \cdot 180\]
\[1{,}080 = 180n - 360\]
\[1{,}440 = 180n\]
\[n = 8\]
The polygon has 8 sides — it is an octagon.
Reference
Mathematics for college students