Question

In the following figure, ΔABC is a triangle such that `(AB)/(AC) = (BD)/(DC)`, ∠B = 70°, ∠C = 50°. Find ∠BAD.

Answer 1

We have, if a line through one vertex of a triangle divides the opposite side in the ratio of the other two sides, then the line bisects the angle at the vertex.

∴ ∠1 = ∠2

In ΔABC

∠A + ∠B + ∠C = 180°

⇒ ∠A + 70 ° + 50° = 180° [∵ ∠B = 70° and ∠C = 50°]

⇒ ∠A = 180° − 120° = 60°

⇒ ∠1 + ∠2 = 60°

⇒ ∠1 + ∠1 = 60° [∵ ∠1 = ∠2]

⇒ 2∠1 = 60°

⇒ ∠1 = 30°

∴ ∠BAD = 30°