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

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Answer 1 · 2017-07-13T12:21:53

Please see below.

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

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

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

In a triangle DeltaABCDeltaABC, ABAB and ACAC are extended and bisectors of exterior angles are drawn to intersect at OO. Find the m/_CBOm/_CBO?