In a ΔABC, the internal bisectors of ∠B and ∠C meet at O. if ∠BAC = 72°, then the value of ∠BOC is:

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Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 2)

Answer 1

Calculation :

F1 Other Arbaz 30-10-23 D13

∠BAC = 72°

By angle sum property

⇒ ∠A + ∠B + ∠C = 180

⇒ ∠B + ∠C = 180 − 72 = 108

⇒ ∠OBC + ∠OCB = 54

The Angular bisectors Meet at O

So By Angle sum property ,

⇒ ∠OBC + ∠OCB + ∠BOC = 180

⇒ 54 + ∠BOC = 180

⇒ ∠BOC = 126

∴ The correct answer is 126°.

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