Since line segment AB is parallel to line segment CD, we can use the corresponding angles postulate to find that angle CPQ is equal to angle QRP. Therefore, angle QRP is 60 degrees.
Since the sum of the angles in a triangle is 180 degrees, we can use this fact to find angle PQR. Angle PQR is equal to 180 - (angle PRB + angle QRP) = 180 - (110 + 60) = 10 degrees.
Finally, since line segment AB is parallel to line segment CD, we can use the alternate interior angles theorem to find that angle DPR is equal to angle PRB. Therefore, angle DPR is 110 degrees.
So, the angles PQR, QRP, and DPR are 10 degrees, 60 degrees, and 110 degrees, respectively.