Geometry and TrigonometryHardNumber of sides from the angle sum
Geometry and Trigonometry practice question
The interior angles of a polygon add up to 1,080°. How many sides does the polygon have?
Answer: 8
The angle sum of a polygon with n sides is (n − 2) × 180. So (n − 2) × 180 = 1,080 gives n − 2 = 6 and n = 8.
Common wrong answers
- If you answered 6
- 6 is n − 2, one step short of the number of sides.
- If you answered 7
- 7 sides would give (7 − 2) × 180 = 900°.
- If you answered 10
- 10 comes from n + 2 = 6 or adding 2 twice; (n − 2) = 6 means n = 8.
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