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Question

In the given figure, O is the centre of the circle. If BOC=120, then x =___.

A
40​​​​​​​
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B
30​​​​​​​
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C
45​​​​​​​
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D
60
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Solution

The correct option is B 30​​​​​​​
AOC+COB=180 (Linear pair)
AOC=180COB
=180120
=60
Since the angle subtended by an arc at the centre of a circle is double the angle subtended by it on any remaining point of the circle, we have
AOC=2×ADC.
ADC=12AOC=602=30


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