Question

6.
The sides BA and CD of a cyclic quadrilateral ABCD
are produced to meet at P, the sides DA and CB are
produced to meet at Q. If angle ADC = 85º and BPC = 40°.
then angle CQD equals:
(A) 50°
(B) 45°
(C) 30°
(D) 75°​

Answer 1

Angle CQD equal to 50°.

Step-by-step explanation:

1. From Δ ADP  

  ∠CDA = ∠DPA+∠PAD   (From sum of interior angle equal to exterior angle)

  Where ∠DPA= 40°   and ∠CDA= 85°

 So

 ∠PAD = 85°-40° = 45°      ...1)

2. ∠PAD + ∠DAB= 180°     ( Linear pair angle)

     So   ∠DAB= 180°- 45°= 135°  

3.  ∠DCB + ∠DAB= 180°    ( Sum of cyclic quadrilateral is 180°)

     ∠DCB = 180°- 135° = 45°

4.  In ΔCDQ

    ∠DCQ +∠CQD + ∠QDC = 180°   (Triangle angle property)

   So  ∠CQD= 180°- 45°- 85°= 50°