Question

Calculate the number of sides of a regular polygon, if: its exterior angle exceeds its interior angle by 60°.

Answer 1

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`