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Question
Calculate the number of sides of a regular polygon, if: its exterior angle exceeds its interior angle by 60°.
Solution
Let interior angle = x
Then exterior angle = x + 60
∴ x + x + 60° = 180°
⇒ 2x = 180° - 60° = 120°
⇒ x = `(120°)/2 = 60°`
∴ Exterior angle = 60° + 60° = 120°
∴ Number of sides = `(360°)/(120°) = 3`
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