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Question

In the given figure, O is the center of the circle, ∠OAB=30o and ∠OCB=55o. Find ∠BOC and ∠AOC respectively.

A
50o,30o
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B
70o,50o
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C
120o,50o
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D
70o,30o
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Solution

The correct option is B 70o,50oGivne ∠OAB=30;∠OCB=55oIn △AOB,AO=OB (both are radius) ∠OBA=∠BAO=30o (angles opposite to equal sides are equal)In △AOB, ∠AOB+∠OBA+∠BAO=180o ∠AOB+30o+30o=180o ∠AOB=180−60=120oNow In △OCB, OC=OB (Radius)∠OCB=∠OBC=55o (Angles opposite to equal sides are equal)In △OCB, ∠COB+∠OCB+∠CBO=180o ∠COB=180−55−55 =180−110 =∠COB=70o=∠BOCFrom ∠AOB=120o∠AOC+∠COB=120o∠AOC+70o=120∠AOC=120−70∠AOC=50o∴∠AOC=50o,=∠BOC=70o

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