Calculate Number Sides Regular Polygon Its Interior Angle Five Times Its Exterior Angle

Calculate the number of sides of a regular polygon, if: (i) its interior angle is five times … its exterior angle exceeds its interior…

Answers:

Let number of sides of a regular polygon = n
(i) Let exterior angle = x
Then interior angle = 5x
x + 5x = 180°
=> 6x = 180°

⇒ x = 180°/6 = 30°

∴ Number of sides (n) = 360°/30° = 12

(ii) Ratio between exterior angle an interior angle = 2 : 7

Let exterior angle = 2x

Then interior angle = 7x

∴ 2x + 7x = 180°

⇒ 9x = 180°

⇒ x = 180°/9 = 20°

∴ Ext. angle = 2x = 2 × 20° = 40°

∴ No. of sides = 360°/40° = 9

(iii) 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