Prove that PQRS is a rectangle, and hence calculate x and y.

here's the solution for 1.4.

To calculate the values of $x$ and $y$, we need to use the geometric properties established in the previous parts and from the diagram (which I'm referencing from our previous conversation).

Let's assume the standard interpretation of the diagram where:

• TQ is tangent to the circle at Q.
• PQRS is a cyclic quadrilateral.
• $PQ \parallel SR$.
• $\angle TQP = x$ (this is $\hat{Q}_1$).
• $\angle QRS = y$.

From the previous parts (1.2 and 1.3, based on the student's clarification):

• **1.2 Prove that