In ΔABC, D is a point on BC. If AB AC = BD DC, ∠B = 75° and ∠C = 45°, then ∠BAD is equal to :

Answer: Option B

Since $$\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}}$$
Hence AD is an angle Bisector
Hence ∠BAD $$=\frac{{180}^{\circ }-\left({75}^{\circ }+{45}^{\circ }\right)}{2}=\frac{{60}^{\circ }}{2}=30^{\circ }$$