Q. 244.3( 4 Votes )

# In the given figure, ABC is a triangle in which::=3:2:1 and AC CD. Find the measure of.

Answer :

60°

Given, ::= 3:2:1 and AC CD

Let, ∠A = 3a

∠B = 2a

∠C = a

In triangle ABC,

∠A + ∠B + ∠C = 180°[Sum of angles of triangle]

⇒ 3a + 2a + a = 180°

⇒ 6a = 180°

⇒ a = 30°

Therefore, ∠C = a = 30°

Now,

∠ACB + ∠ACD + ∠*E*CD = 180°[Sum of angles of triangle]

⇒ 30° + 90° + ∠*E*CD = 180°

⇒ ∠*E*CD = 60°

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