Question

in the given figure the bisectors of the <ABC and <BCA intersect each other at point o. if <NOC=110°,the <A is​

Answer 1

In triangle ABC,

∠A+∠B+∠C=180

∘

..... (1)

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

∘

..... (2)

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

2

1

∠A+90

∘

=∠BOC