Question

find the x,y and z....

Answer 1

hey
here's your answer !!

AB is || to CD.

now angle CQP and angle PQR sum up to 180 degree ( angle CQR )

So , angle CQP + angle PQR = angle CQR
=> 120 degree + angle PQR = 180 degree
=> angle PQR = 60 degree.

now, angle PQR and angle APQ are alternate angles
so , angle PQR = angle APQ.
so, x = 60 degree.

now angle DRP and angle QRP sum up to 180 degree ( angle CQR )

So , angle DRP + angle QRP = angle QRD
=> 115 degree + angle QRP = 180 degree
=> angle QRP = 65 degree.

now, angle QRP and angle BPR are alternate angles
so , angle QRP = angle BPR
so, z = 65 degree.

Now in triangle PQR ,
angle QRP + angle PQR + angle QPR = 180 degree

65 degree + 60 degree + x = 180 degree
=> 125 degree + x = 180 degree
=> x = 55 degree.

Hope it helps !!