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

Question

In &#x394; ABC , if bisectors of &#x2220; ABC and &#x2220; ACB intersect at O angle of 120&#xB0;, then find the measure of &#x2220; A .

Philoid · Accepted 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