Question

in triangle abc is bisector of angle abc and angle acb intersect at o at angle of 120 degree then find the measure of angle a

Answer 1

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)

Answer 2

Answer:

∠A = 60°

Step-by-step explanation:

In ΔBQC

∠BOC + ∠OBC + ∠OCB = 180°

120° + 1/ 2 ∠B + 1 /2∠C = 180°

1 /2 (∠B + ∠C) = 60°

∠B + ∠C = 120° (i)

In ΔABC ∠A + ∠B + ∠C = 180°

∠A + 120° = 180°[From (i)]

∠A = 60°

i hope it helps !!!!!!!!!!!!