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in Triangles by (56.3k points)

In △ABC, if ∠B = 60°, ∠C = 80° and the bisectors of angles ∠ABC and ∠ACB meet at point O, then find the measure of ∠BOC.

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∠B = 60°, ∠C = 80° 

As per question: ∠OBC = 60°/2 = 30° and 

∠OCB = 80°/2 = 40° 

In triangle BOC, 

∠OBC + ∠OCB + ∠BOC = 180° [Sum of angles of a triangle = 180°] 

30° + 40° + ∠BOC = 180° 

∠BOC = 110°

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