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

1 Answer
Jul 13, 2017

Please see below.

Explanation:

Let the figure appear as shown below.

enter image source here

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#