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Question

# For the given figure, find ∠ABC+∠ACB, where O is the centre of the circle.

A
40o
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B
120o
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C
140o
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D
180o
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Solution

## The correct option is C 140oThe given figure is as follows: Here, OB=OC= radius of the circle ∴△OBC is a isosceles triangle. ⇒∠OBC=∠OCB=50o From interior angle sum property for △OBC, ∠BOC=180o−50o−50o=80o We know, the angle subtended by an arc at the centre of a cirlce is double the angle subtended by the arc at any point on the circle. ∴∠BOC=2×∠BAC ⇒∠BAC=80o2=40o From interior angle sum property for △ABC, ∠ABC+∠ACB=180o−∠BAC ⇒∠ABC+∠ACB=180o−40o=140o

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