Question

in triangle abc the bisector of angle abc and angle BCA intersect each other at O the measure of angle BOC is​

Answer 1

Answer:

In triangle ABC,

∠A+∠B+∠C=180

OB and OC are bisectors of ∠B and ∠C

So, ∠B=2∠OBC

and ∠C=2∠OCB

Now equation (1) can be written as,

∠A+2(∠OBC+∠OCB)=180

In triangle OBC,

∠BOC+∠OBC+∠OCB=180

∠OBC+∠OCB=180

−∠BOC..........(3)

From (2) and (3)

∠A+2(180

−∠BOC)=180

∠A+360

−2∠BOC=180

∠A+180

=2∠BOC

∠A+90

=∠BOC= 90°