Question

In a triangle `DeltaABC`, `AB` and `AC` are extended and bisectors of exterior angles are drawn to intersect at `O`. Find the `m/_CBO`?

Answer 1

Please see below.

Explanation:

Let the figure appear as shown below.

Now `m/_CBO=1/2/_CBP=1/2(m/_A+m/_ACB)`

similarly `m/_BCO=1/2/_BCQ=1/2(m/_A+m/_ABC)`

adding the two

`m/_CBO+m/_BCO=1/2(m/_A+m/_ACB+m/_ABC+m/_A)`

= `1/2(180^@+m/_A)=90^@+1/2m/_A`

and `m/_BOC=180^@-(m/_CBO+m/_BCO)`

= `180^@-(90^@+1/2m/_A)`

= `90^@-1/2m/_A`