In a △ABC, the internal bisectors of ∠B and ∠C meet at O. If ∠BAC = 72°, then the value of ∠BOC is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 126°.
Now,
⇒ ∠B + ∠C = 180° - 72° = 108°
OB and OC are bisectors of B and C respectively
⇒ ∠OBC + ∠OCB = 1/2(∠B + ∠C)
⇒ 1/2 × 108° = 54°
In △OBC,
⇒ ∠OBC + ∠OCB + ∠BOC = 180°
⇒ 54° + ∠BOC = 180°
⇒ ∠BOC = 180° - 54° = 126°