Question

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

Answer 1

In ΔABC, ∠B = 60, ∠C = 80 and the bisectors of  ∠B and ∠C meet at O.

We need to find the measure of  ∠BOC 

Since,BO is the bisector of  ∠B

∠OBC = 1/2 ∠B

          `= 1/2 (60°)`

           = 30°

Similarly,CO is the bisector of  ∠C

`∠OCB 1/2 ∠C`

= 1/2(80°)

 = 40°

Now, applying angle sum property of the triangle, in ΔBOC, we get,

∠OCB + ∠OBC + ∠BOC = 180°

            30° + 40° + ∠BOC = 180°

                      ∠BOC + 70° = 180°

                                ∠BOC = 180°- 70°

                                            = 110°

Therefore, ∠BOC = 110°.