Identify parallel lines and transversals. Given PQ parallel RS and QU parallel PT. If angle PSR = 42^ circ, find x ( angle PQU).

We are given that line PQ is parallel to line RS ($PQ \parallel RS$).
We are also given that line QU is parallel to line PT ($QU \parallel PT$).
The angle $\angle PSR = 42^\circ$. We need to find angle $x$, which is $\angle PQU$.

Consider the parallel lines $PQ$ and $RS$ intersected by the transversal $QU$.
The angles $\angle PQU$ (which is $x$) and $\angle QUS$ are alternate interior angles.
Therefore, they are equal: