Question 128

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

Solution

Let angles of $$\triangle$$ABC be $$\angle$$A =$$2\theta$$ , $$\angle$$B = $$3\theta$$ and $$\angle$$C = $$4\theta$$

=> $$\angle$$A + $$\angle$$B + $$\angle$$C = 180°

=> $$2\theta + 3\theta + 4\theta$$ = 180°

=> $$\theta = \frac{180}{9}$$ = 20°

=> $$\angle$$A = 2*20 = 40°

Since, AB | | CD

=> $$\angle$$ACD = $$\angle$$BAC [Alternate angles]

=> $$\angle$$ACD = 40°

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