In a ΔABC ∠A : ∠B : ∠C = 2 : 3 : 4. A line CD drawn || to AB, then the ∠ACD is :

Answer: Option A

According to question,

Given :
∠A + ∠B + ∠C = 180°
2 + 3 + 4 = 9 units
∴ 9 units = 180°
   1 unit = 20°
∴ ∠A = 2 × 20° = 40°
   ∠B = 3 × 20° =60°
   ∠C = 4 × 20° = 80°
and AB || CD
   ∠B = ∠C
∴ ∠ACD = 180° - 60° - 80°
   ∠ACD = 40°