In a ∆ ABC ∠A : ∠B : ∠C = 2 : 3 : 4. A

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

1. 40°
2. 60°
3. 80°
4. 20°

Correct Option: B

According to question , we draw a figure of ∆ ABC
Given , ∠A : ∠B : ∠C = 2 : 3 : 4
Let ∠A = 2y , ∠B = 3y , ∠C = 4y
In ∆ ABC ,
We know that , 2y + 3y + 4y = 180°
⇒ 9y = 180°
⇒ y = 20°
∴ Angles of triangle are 40°, 60° and 80°

AB || CD
∠DCE = ∠ABC = 60°
∴ ∠ACB + ∠ACD + ∠DCE = 180°
⇒ ∠ACD = 180° – 120° = 60°