Question

In triangle ABC, if bisectors of angle abc and angle acb intersect at o at angle 120.then find the measure of angle A​

Answer 1

Hi,This is your Answer Happy Learning.

Answer 2

Given :- In triangle ABC, bisectors of ∠ABC and ∠ACB intersect at O at angle 120° .

To Find :-

• ∠A = ?

Solution :-

we know that, when angle bisector meets inside a ∆,

• ∠BOC = 90° + (1/2) (∠BAC) .

Proof :-

we have,

∠ABO = ∠OBC, ∠ACO = ∠OCB (By angle bisector.)

In ΔABC,

→ ∠A + ∠B + ∠C = 180° (By angle sum Property.)

→ ∠A + 2∠OBC + 2∠OCB = 180°

→ 2(∠OBC + ∠OCB) = 180° - ∠A

→ ∠OBC + ∠OCB = 90° - (1/2)∠A

Now in ΔBOC,

→ ∠OBC + ∠OCB +∠BOC = 180°

→ 90 - (1/2)∠A + ∠BOC = 180°

→ ∠BOC = 90° + (1/2)∠A

→ ∠BOC = 90° + (1/2)∠BAC .

therefore,

→ 120° = 90° + (1/2)∠BAC

→ 120° - 90° = (1/2)∠BAC

→ 30° = (1/2)∠BAC

→ ∠BAC = 60° (Ans.)

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