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Question

In the triangle ABC, the bisectors of the exterior angle B and C meet at O. Given BAC=60 and ABC=70. Find BOC.

A
60
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B
66
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C
55
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D
80
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Solution

The correct options are
A 60
C 55
In ABC,

ABC+BAC+ACB=180

60+70+ACB=180

ACB=50
ext.B=180ABC

2OBC=18070 (BOB bisects ext.B)

OBC=55
Similarly, OCB=65

Now, In OBC,

OCB+OBC+BOC=180

65+55+BOC=180

BOC=180120

BOC=60

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