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Question

In the given figure, O is the centre of the circle, and OAB=20° and OCB=50°. Find AOC.


A
60°
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B
70°
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C
50°
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D
20°
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Solution

The correct option is A 60°
OA=OC (radii of the same circle)
OAB=OBA=20°
In OAB,
OAB+AOB+BOA=180°
20°+20°+BOA=180°
BOA=140°
OB=OC (radii of the same circle)
OBC=OCB=50°
In OCB,
OBC+OCB+COB=180°
50°+50°+COB=180°
COB=80°
AOB=AOC+BOC
AOC=AOBBOC
AOC=140°80°
AOC=60°

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