In ΔABC, D and E are the points on AB and AC respectively such that AD × AC = AB × AE. If ∠ADE = ∠ACB + 30° and ∠ABC = 78°, then ∠A = ?

Answer: Option D

$$\frac{\text{AD}}{\text{AB}}=\frac{\text{AE}}{\text{AC}}$$
(It's mean ΔADE ∽ ΔABC)
∠B = ∠D, ∠C = ∠E
∠D = 78°
∠ADE = ∠ACB + 30°
78° = ∠ACB + 30°
∠ACB = 48°
∠A + ∠D + ∠E = 180°
∠A + 78 + 48 = 180°
∠A = 54°