In the given figure, BO and CO are the bisectors of ∠B and ∠C respectively. If ∠A = 50°, then ∠BOC = ?

Question

In the given figure, BO and CO are the bisectors of ∠ B and ∠ C respectively. If ∠ A = 50°, then ∠ BOC = ?

Philoid · Accepted Answer

In ∆ABC,

∠A + ∠B + ∠C=180°

50° + ∠B + ∠C=180°

∠B + ∠C=180°−50°=130°

∠B = 65°

∠C = 65°

Now in ∆OBC,

∠OBC + ∠OCB + ∠BOC=180°

∠BOC = 180° – 65° (∠OBC + ∠OCB = 65 because O is bisector of ∠B and ∠C)

= 115°