Question

if bisector of angle B and angle C of a triangle ABC. meet at O . prove angle BOC = 90 + 1/2 angleA

Answer 1

Hey Dear..

Here is your answer ☺

⏩(Please refer to the attached image)

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)

⏩Hence Proved⏩

Hope it helps you out ⭐^_^⭐
Thanks ⭐☺⭐(^^)⭐