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Question

In the given figure, if AOC=120, then ABC = _______.


A
50
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B
120
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C
60
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D
100
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Solution

The correct option is B 120

Given that AOC=120.

Consider the arc ABC. Take a point on the circumference of the circle outisde this arc. Join AP and PC.

Arc ABC subtends AOC at centre and APC on the remaining part of the circle at a point P.
Since the angle subtended by an arc at the centre is double the angle subtended by it on any remaining part of the circle,
APC=12AOC=12×120=60
Consider the cyclic quadrilateral APCB. Since opposite angles are supplementary,
ABC+APC=180.
ABC=180APC=18060=120


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