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Question

In the figure, if AOB=80o and ABC=30o, then find CAO.

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Solution

In the figure, AOB=80o, ABC=30o

Arc AB subtends AOB at the centre and ACB at the remaining part of the circle.

ACB=12AOB=12×80o=40o

In ΔOAB, OA=OB

OAB=OBA

But, OAB+OBA+AOB=180o

OAB+OBA+80o=180o

OAB+OAB=180o80o=100o

2OAB=100o

OAB=100o2=50o

Similarly, in ΔABC,

BAC+ACB+ABC=180o

BAC+40o+30o=180o

BAC=180o30o40o

=180o70o=110o

CAO=BACOAB

=110o50o=60o


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