**AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = 20° ; find : ( … angle (iii) the number of sides in…**

###### Answers:

∵ Polygon is regular (Given)

∴ AB = BC

⇒ ∠BAC = ∠BCA

[∠s opp. To equal sides]

But ∠BAC = 20°

∴ ∠BCA = 20°

i.e. in triangle 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

∴ 360°/n = 40°

n = 360°/40° = 9

n = 9

∴ (i) 140° (ii) 9