Question

BO and CO are angle bisctors. If <A = 50 degree, then <BOC = ?​

Answer 1

Answer:

As BO and CO are the angle bisectors of external angles of△ABC, Then

∠1=∠2

∠4=∠3

We know, ∠A+∠ABC+∠ACB=180

∘

…eqn(1)

And ∠ABC=180−2∠1

∠ACB=180−2∠4

Putting it in the eqn (1), we get

∠A+180−2∠1+180−2∠4=180

⇒∠1+∠4=90+

2

1

∠A…eqn(2)

Also we know from the figure, ∠BOC+∠1+∠4=180

∘

∠BOC=180−∠1−∠4

From eqn (2)

∠BOC=180−90−

2

1

∠A

⇒∠BOC=90

∘

−

2

1

∠A