Answer :

Given: CD||AB and BAD = 30°


Consider ΔABD


ADB = 90° (angle in semicircle)


Now, by angle sum property


ABD + BAD + ADB = 180°


ABD + 30° + 90° = 180°


ABD = 180° – 30° – 90°


ABD = 60°


Here,


ABD + ACD = 180° (opposite angles in cyclic quadrilateral are supplementary)


60° + ACD = 180°


BCD = 180° – 60°


BCD = 120°


Here, CD||AB and AC is the transversal


CAB + ACD = 180° (interior angles along the transversal are supplementary)


CAB + 120° = 180°


ABC = 180° – 120° = 60°


ABC = 60°


ABC = CAD + DAB


60° = CAD + 30°


CAD = 60° – 30° = 30°


CAD = 30°

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