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

Question

In a &#x394; ABC , If &#x2220; A = 60&#xB0;, &#x2220; B =80&#xB0; and the bisectors of &#x2220; B and &#x2220; C meet at O , then &#x2220; BOC =

Philoid · Accepted Answer

In

∠A + ∠B + ∠C = 180^o

60^o + ∠B + ∠C = 180^o

∠B + ∠C = 120^o

∠B + ∠C = 60^o (i)

∠BOC + ∠OBC + ∠OCB = 180^o

∠BOC + ∠B + ∠C = 180^o

∠BOC + (∠B + ∠C) = 180^o

∠BOC + 60^o = 180^o [From (i)]

∠BOC = 120^o