Question

In a Δ ABC, If ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =

A. 60°

B. 120°

C. 150°

D. 30°

Answer 1

In ΔABC

∠A + ∠B + ∠C = 180°

60° + ∠B + ∠C = 180°

∠B + ∠C = 120°

\(\frac{1}{2}\)∠B + \(\frac{1}{2}\)∠C = 60°(i)

∠BOC + ∠OBC + ∠OCB = 180°

∠BOC + \(\frac{1}{2}\)∠B + \(\frac{1}{2}\)∠C = 180°

∠BOC + \(\frac{1}{2}\)(∠B + ∠C) = 180°

∠BOC + 60° = 180°[From (i)]

∠BOC = 120°