Answer :

Given AOB = 90° and ABC = 30°


We know that angles opposite to equal sides are equal.


⇒∠OAB = ABO


By angle sum property,


⇒∠OAB + ABO + BOA = 180°


2 OAB + BOA = 180°


2 OAB + 90° = 180°


2 OAB = 180° - 90° = 90°


⇒∠OAB = 90°/ 2


OAB = 45°


We know that angles subtended by an arc at the centre of the circle is double the angle subtended by it to any other part of the circle.


C = 45°


By angle sum property,


⇒∠ABC + BCA + ACB = 180°


30° + 45° + CAB = 180°


75° + CAB = 180°


⇒∠CAB = 180° - 75°


CAB = 105°


Also CAB = CAO + OAB


105° = CAO + 45°


⇒∠CAO = 105° - 45°


CAO = 60°

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