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ABCD is a cyclic trapezium with AB || DC and AB = diameter of the circle. If ∠CAB = 30° then ∠ADC is   (SSC CGL 2nd Sit.  2013)
  • a)
    60°
  • b)
    120°
  • c)
    150°
  • d)
    30°
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
ABCD is a cyclic trapezium with AB || DC and AB = diameter of the circ...

AB is a diameter of the circle
∴ ∠ACB = 90° {Angle made by the diameter on the semicircle
∠BAC = 30° {given)
∴ ∠BAC = ∠ACD = 30°   {As AB || CD}.
∠BCD = 90° + 30° = 120°
As ABCD is cyclic quadrilateral
∴ ∠BAD + ∠BCD = 180°
∠BAD + 120° = 180°
∠BAD = 180° – 120° = 60°
∠BAD = ∠CAB + ∠CAD = 60°
30° + ∠CAD = 60°  ⇒ ∠CAD = 30°
Again, AB || CD, ∴ ∠BAD + ∠ADC = 180°
60° + ∠ADC = 180°
∴ ∠ADC = 180° – 60° = 120°.
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ABCD is a cyclic trapezium with AB || DC and AB = diameter of the circle. If ∠CAB = 30° then ∠ADC is (SSC CGL 2nd Sit. 2013)a)60°b)120°c)150°d)30°Correct answer is option 'B'. Can you explain this answer?
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