In Δ ABC, it is given that AB/AC = BD/DC. If . . .

Question : In Δ ABC, it is given that AB/AC = BD/DC. If ∠B=70° and ∠C=50°, then ∠BAD is
a) 30°
b) 40°

c) 45°

d) 50°

Doubt by Saumya

Hint : Use Internal Angle Bisector Theorem

Solution : 

∠B=70° (Given)
∠C=50° (Given)

AB/AC = BD/DC (Given)

∠BAD = ∠CAD
(Converse of Internal Angle Bisector Theorem)

Let 
∠BAD = ∠CAD = x

Now, In ΔBAC

∠ABC + ∠BCA + ∠BAC = 180°
(Angle Sum Property)

∠ABC + ∠BCA + ∠BAC = 180°

70°+50°+x+x = 180°
120°+2x = 180°
2x = 180°-120°
2x = 60°
x = 60°/2
x = 30°

∠BAD = 30°

Hence, a) would be the correct option.