Question

If the bisectors of angle ABC .and angle Acb of a triangle ABC meet at O prove that angle BOC= 90 degree + 1/2 angle A

Answer 1

Answer:

In ΔABC, by angle sum property we have

2x + 2y + ∠A = 180°

⇒ x + y + (∠A/2) = 90°

⇒ x + y = 90° –  (∠A/2)  à (1)

In ΔBOC, we have

x + y + ∠BOC = 180°

90° – (∠A/2) + ∠BOC = 180° [From (1)]

∠BOC = 180° – 90° + (∠A/2)

∠BOC = 90° + (∠A/2)