Q. 65.0( 4 Votes )

# In Δ *ABC*, if bisectors of ∠*ABC* and ∠*ACB* intersect at *O* angle of 120°, then find the measure of ∠*A*.

Answer :

In

∠BOC + ∠OBC + ∠OCB = 180^{o}

120^{o} + ∠B + ∠C = 180^{o}

(∠B + ∠C) = 60^{o}

∠B + ∠C = 120^{o} (i)

In

∠A + ∠B + ∠C = 180^{o}

∠A + 120^{o} = 180^{o} [From (i)]

∠A = 60^{o}

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