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ABCD is a cyclic trapezium with AB || DC and AB is diameter of the circle. If ∠CAB = 50° then ∠ADC is –
- a)40°
- b)70°
- c)140°
- d)150°
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
ABCD is a cyclic trapezium with AB || DC and AB is diameter of the cir...
We can see from the figure that,
ΔABC is right angled triangle,
⇒ ∠ABC = 90° - ∠CAB = 90° - 50° = 40°
Now,
∵ ABCD is a cyclic quadrilateral,
Opposite angles are supplementary.
⇒ ∠ABC + ∠ADC = 180°
⇒ 40° + ∠ADC = 180°
⇒ ∠ADC = 140°
∴ ∠ADC = 140°
Most Upvoted Answer
ABCD is a cyclic trapezium with AB || DC and AB is diameter of the cir...
We can see from the figure that,
ΔABC is right angled triangle,
⇒ ∠ABC = 90° - ∠CAB = 90° - 50° = 40°
Now,
∵ ABCD is a cyclic quadrilateral,
Opposite angles are supplementary.
⇒ ∠ABC + ∠ADC = 180°
⇒ 40° + ∠ADC = 180°
⇒ ∠ADC = 140°
∴ ∠ADC = 140°
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ABCD is a cyclic trapezium with AB || DC and AB is diameter of the cir...
ABCD is a cyclic trapezium with AB || DC and AB is the diameter of the circle, then angle DAB is a right angle.
We know that in a cyclic trapezium, the opposite angles are supplementary. Since AB || DC, angle DAB and angle BCD are opposite angles. Therefore, angle DAB + angle BCD = 180 degrees.
Furthermore, since AB is the diameter of the circle, angle BCD is a right angle (since it is inscribed in a semicircle). Therefore, angle DAB + 90 degrees = 180 degrees.
Simplifying the equation, we get angle DAB = 90 degrees. Hence, angle DAB is a right angle.
We know that in a cyclic trapezium, the opposite angles are supplementary. Since AB || DC, angle DAB and angle BCD are opposite angles. Therefore, angle DAB + angle BCD = 180 degrees.
Furthermore, since AB is the diameter of the circle, angle BCD is a right angle (since it is inscribed in a semicircle). Therefore, angle DAB + 90 degrees = 180 degrees.
Simplifying the equation, we get angle DAB = 90 degrees. Hence, angle DAB is a right angle.
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ABCD is a cyclic trapezium with AB || DC and AB is diameter of the circle. If ∠CAB = 50° then ∠ADC is –a)40°b)70°c)140°d)150°Correct answer is option 'C'. Can you explain this answer?
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