A question on circular measure, SERIOUSLY urgent.

http://www.flickr.com/photos/13256126@N0…

Based on the diagram from the link above, TPU is a common tangent to two circles at the point P. MPS and NPQ are straight lines. Calculate the values of y and z only.

x is well, 40 through the alternate segment rule and I'm just clueless as to how to solve the remaining two questions.

I take it that missing point N is the vertex of angle y. I will also take it that you mean it when you say that NPS is a straight line, although it does not appear so in the sketch.

y = MPT ... (angles in same segment)
= UPS ... (vertical angles)
= PRS ... (angles in same segment)
= 60°

QPS = MPN ... (vertical angles)
= 180° - PMN - y ... (angle sum of triangle)
= 180° - 40° - 60°
= 80°

TPR = 115° - TPM
= 115° - 80°
= 35°

RSP = TPR ... (angles in same segment)
= 35°

z = 180° - TPR - QPS ... (angle sum of triangle)
= 180° - 35° - 80°
= 65°