https://cracku.in/cat/history/1269514. Can u Please elaborate on the solution of the 5th Question.

Hi Balu Akula,
In the figure given in the solution Let Angle QRS = x.
Since QR = QC, Angle QCR = x.
Angle CQS = Angle CSQ = 180-x/2 = 90-0.5x
Angle CQR = 180-x-x = 180-2x
Angle CQP = Angle CPQ = 180-(180- 2x) = 2x.
Angle PCQ = 180-2x-2x = 180-4x.
Angle PCT = 180-(180-4x)-x = 3x
Angle PTC = (180-3x)/2 = 90-1.5x
(90-1.5x)/(90-0.5x) = 1/2
x = 36 degrees
Angle PUQ = 180-(Angle PCQ)/2 = 180-(180-144)/2 = 162