Question

In ∆ABC, ∠A = 60°, ∠B = 80°, and the bisectors of ∠B and ∠C, meet at O. Find

(i) ∠C

(ii) ∠BOC

Answer 1

(i) We know that the sum of all three angles of a triangle is 180°.

Hence, for △ABC, we can say that:

∠A + ∠B + ∠C = 180° (Sum of angles of ∆ABC)

60° + 80° + ∠C= 180°.

∠C = 180° – 140°

∠C = 140°.

(ii) For △OBC,

∠OBC = ∠B/2 = 80/2 (OB bisects ∠B)

∠OBC = 40°

∠OCB =∠C/2 = 40/2 (OC bisects ∠C)

∠OCB = 20°

If we apply the above logic to this triangle, we can say that:

∠OCB + ∠OBC + ∠BOC = 180° (Sum of angles of △OBC)

20° + 40° + ∠BOC = 180°

∠BOC = 180° – 60°

∠BOC = 120°