Question

AB, BC and CD are the three consecutive
sides of a regular polygon. If angle BAC = 15°;
find.
1. each interior angle of the polygon.
2. each exterior angle
3.number of sides of the polygon​

Answer 1

Step-by-step explanation:



∵ 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