Question

in the given figure BO and CO are the bisectors of the exterior angles meeting each other at O. if angle a =7 0 degrees find angle BOC

Answer 1

This is the direct formula for finding this type of questions .
If you want to proof of this formula I can give you.

Answer 2

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+1/2∠A…eqn(2)

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

∠BOC=180−∠1−∠4

From eqn (2)

∠BOC=180−90−1/2∠A

⇒∠BOC=90°1/2∠A