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  • Inthe adjoining figure, ABCD is a cyclic quadrilateral and AOB is diameter. If ∠ ADC = 120° then ∠ BAC = <img alt="" src="https://cdn.entrance360.com/media

Inthe adjoining figure, ABCD is a cyclic quadrilateral and AOB is diameter. If ∠ ADC = 120° then ∠ BAC =

Option: 1

120°


Option: 2

90°


Option: 3

60°


Option: 4

30°


Answers (1)

best_answer

∠ ABC +  ∠ ADC = 180°   (opposite angle of of cyclic quad)

∠ ABC + 120° = 180°

∠ ABC = 60°

Also, ∠ ACB = 90°    (angle in a semicircle)

In triangle ABC

∠ ABC + ∠ ACB + ∠ BAC = 180°

60° + 90° + ∠ BAC = 180°

∠ BAC = 30°

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