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

Question

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

Philoid · Accepted 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 + ∠ECD = 180°[Sum of angles of triangle]

⇒ 30° + 90° + ∠ECD = 180°

⇒ ∠ECD = 60°