In the given figure, 2b−a=65o and ∠BOC=90o, find the measure of ∠AOB,∠AOD and ∠COD.
A
∠AOB=35o
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B
∠AOD=100o
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C
∠COD=135o
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D
All of the above
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Solution
The correct option is D All of the above Given, ∠BOC=90oand2b−a=65o From the figure, ∠AOB+∠AOD+∠BOC+∠COD=360o =>a+2b+90o+(2a+b+15)=360o =>a+b=85o Add the given equation with this equation, we get 2b−a+a+b=65o+85o b=50o then, a=85o−b=85o−50o=35o ∠AOB=ao=35o,∠AOD=2bo=2×50o=100o ∠COD=(2a+b+15)=2×35o+50o+15=135o