Question

AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = 20° ; find :

(i) its each interior angle,
(ii) its each exterior angle
(iii) the number of sides in the polygon.

Answer 1

∵ Polygon is regular  (Given)

∴ AB = BC

⇒ ∠BAC = ∠BCA   ...[∠S opposite to equal sides]

But ∠BAC = 20°

∴ ∠BCA = 20°

i.e. In Δ ABC,

∠B + ∠BAC + ∠BCA = 180°

∠B + 20° + 20° = 180°

∠B = 180° - 40°

∠B = 140°

(i) each interior angle = 140°

(ii) each exterior angle = 180°- 140°= 40°

(iii) Let no. of. sides = n

`therefore 360^circ/"n" = 40^circ`

n = `360^circ/40^circ = 9`

n = 9