Determine the number of sides of a polygon whose exterior and interior

1.	Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.
Answer» By using the formulas, The sum of interior angles of a polygon = (n – 2) × 180° ……..(i) The Sum of exterior angle of a polygon is 360° We know that Sum of exterior angles/Sum of interior angles = 1/5…..(ii) So, equating (i) and (ii) we get 360^o/(n – 2) × 180° = 1/5 On cross multiplication, (n – 2) × 180° = 360^o × 5 (n – 2) × 180° = 1800^o (n – 2) = 1800^o/180^o (n – 2) = 10 n = 10 + 2 = 12 ∴ Numbers of sides of a polygon is 12.

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.

Answer»

By using the formulas,

The sum of interior angles of a polygon = (n – 2) × 180° ……..(i)

The Sum of exterior angle of a polygon is 360°

We know that Sum of exterior angles/Sum of interior angles = 1/5…..(ii)

So, equating (i) and (ii) we get

360^o/(n – 2) × 180° = 1/5

On cross multiplication,

(n – 2) × 180° = 360^o × 5

(n – 2) × 180° = 1800^o

(n – 2) = 1800^o/180^o

(n – 2) = 10

n = 10 + 2

= 12

∴ Numbers of sides of a polygon is 12.