2011 Pascal Problem 20

In the diagram, PR, PS, QS, QT, and RT are straight line segments. QT intersects PR and PS at U and V, respectively. If PU = PV, \angle UPV = 24^\circ, \angle PSQ = x^\circ, and \angle TQS = y^\circ, what is the value of x + y?

\textbf{(A)}\ 48\quad \textbf{(B)}\ 66\quad \textbf{(C)}\ 72\quad \textbf{(D)}\ 78\quad \textbf{(E)}\ 156

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Full credit to this problem is given to the CEMC, you may view all Pascal contests here.