Properties of Angles Formed by Two Parallel Lines and a Transversal
Draw four lin...
Question
Draw four lines OA,OB,OC,OD in order, ∠AOB=48o, ∠COD=34o. OP bisects ∠AOB, OQ bisects ∠COD. If OQ is perpendicular to OP, calculate ∠BOC.
A
49o
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B
50o
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C
51o
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D
48o
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Solution
The correct option is A49o Since OP is the angle bisector of ∠AOB, we have ∠POB=482=24o Similarly, since OQ is the angle bisector of ∠COD, we have ∠COQ=342=17o Now, ∠POQ=∠POB+∠BOC+∠COQ Given, ∠POQ=90o =>∠POB+∠BOC+∠COQ=90o =>24o+∠BOC+17o=90o =>∠BOC=49o