Question

In given figure. BO and CO are the bisectors of /_B and /_C respectively.If /_A=50^(@) then /_BOC=? a 130^(@) b100^(@) c115^(@) d120^(@)​

Answer 1

Answer:

Correct option is

A

90o−21∠A

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+21∠A…eqn(2)

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

∠BOC=180−∠1−∠4

From eqn (2)

∠BOC=180−90−21∠A⇒∠BOC=90∘−21∠A