Question

In Fig. 4.58, 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°