Question

If ∠ACD = 114º and ∠ABC = 1/2 ∠BAC What is the value of ∠ABC ?​

Answer 1

Solution :-

Let us assume that, ∠BAC is equal to 2x .

So,

→ ∠ABC = (1/2)∠BAC

→ ∠ABC = (1/2) * 2x

→ ∠ABC = x

also, given that,

→ ∠ACD = 114°

then,

→ ∠ABC + ∠BAC = ∠ACD { Exterior angle is equal to sum of opposite interior angles }

→ x + 2x = 114°

→ 3x = 114°

→ x = 38° (Ans.)

Hence, the value of ∠ABC is equ to 38° .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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