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Question

In the given figure, O is the centre of the circle. Find x.


A

50

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B

40

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C

30

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D

20

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Solution

The correct option is B

40


The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

GivenABC=50,
AOC=2 ABC=2×50=100


Also, since OA and OC are radii of the circle, OA=OC.
OAC=OCA

In AOC,

x+x+AOC=180.

2x=180AOC=180100=80

x=40


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