Using the provided diagram and angle measures, prove that PT is parallel to QS.

Here's the solution to question 3:

a) Prove that $PT \parallel QS$

Step 1: Identify given parallel lines and angles.
We are given that $PU \parallel QT$.
We are given the following angles:
$\angle UPT = x$
$\angle QPT = x+40^\circ$
$\angle PQT = y$
$\angle QTS = 42^\circ$
$\angle RQS = 82^\circ$

Step 2: Use properties of parallel lines $PU \parallel QT$.
Since $PU \parallel QT$ and $PT$ is a transversal, the alternate interior angles are equal:

$$\angle UPT = \angle PTQ$$ $$$$