Question

In a triangle abc, ob and oc are the angle bisectors of b and c. If boc is 122. Find

Answer 1

Answer:

∠A = 64°

Step-by-step explanation:

In a triangle abc, ob and oc are the angle bisectors of b and c. If boc is 122. Find  ∠A

Let say ∠B  = 2X

&  ∠C = 2Y

Then OB being angle bisectors of b

=> ∠OBC = 2X/2 = X

Similarly

∠OCB = 2Y/2 + Y

in Δ OBC

∠BOC + ∠OBC + ∠OCB = 180°

=> 122 + X + Y = 180°

=> X + Y = 58°

in ΔABC

∠A + ∠B + ∠C = 180°

=> ∠A + 2X + 2Y = 180°

=> ∠A + 2(X + Y) = 180°

=> ∠A + 2(58) = 180°

=> ∠A = 64°

Answer 2

In a triangle abc, ob and oc are the angle bisectors of b and c. If boc is 122. Find  ∠A

Let say ∠B  = 2X &  ∠C = 2Y

Then OB being angle bisectors of b

=> ∠OBC = 2X/2 = X

Similarly

∠OCB = 2Y/2 + Y

in Δ OBC

∠BOC + ∠OBC + ∠OCB = 180°

=> 122 + X + Y = 180°

=> X + Y = 58°

in ΔABC

∠A + ∠B + ∠C = 180°

=> ∠A + 2X + 2Y = 180°

=> ∠A + 2(X + Y) = 180°

=> ∠A + 2(58) = 180°

=> ∠A = 64°