In a Δ ABC, If ∠A = 60°, ∠B = 80° and the bisectors of ∠B and

1.	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» 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°

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»

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°