Answer :

(i)


ABCD is a cyclic quadrilateral.


BAD + BCD = 180°


BAD + 120° = 180°


BAD = 60°


(ii)


BDA = 90°[Angle in a semi-circle]


In triangle ABD,


ABD + BDA + BAD = 180°[Sum of angles of triangle]


ABD + 90° + 60° = 180°


ABD + 150° = 180°


ABD = 30°


(iii)


OD = OA [Radius]


OAD = ODA = BAD = 180°


ODB = 90° - ODA


ODB = 90° - 60°


ODB = 30°


(iv)


ADC = ADB + CDB


ADC = 90° + 30°


ADC = 120°


In triangle AOD,


AOD + OAD + ODA = 180°[Sum of angles of triangle]


AOD + 60° + 60° = 180°


AOD + 120° = 180°


AOD = 60°


Triangle AOD is an equilateral triangle.


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