In the diagram, QR is parallel to TP and angle WPT = 88 degrees. Find the value of x.

We are given that line $BA$ is parallel to line $DE$ ($BA \parallel DE$).
We have $\angle ABC = 52^\circ$.
The reflex angle at $D$ is $312^\circ$.
We need to find the value of $x$, which represents the reflex angle at $C$.

The sum of angles around a point is $360^\circ$.
The interior angle at $D$, $\angle CDE$, is given by:

Let's draw a line $FCH$ passing through $C$, such that $FCH \parallel BA$ and $FCH \parallel DE$.

Considering $BC$ as a transversal cutting parallel lines $BA$ and $FCH$:

Since $\angle ABC = 52^\circ$, we have:

Considering $CD$ as a transversal cutting parallel lines $FCH$ and $DE$:

Since $\angle CDE = 48^\circ$, we have:

From the diagram, the interior angle $\angle BCD$ is the sum of $\angle BCF$ and $\angle DCH$:

The angle $x^\circ$ is the reflex angle at $C$. The sum of angles around a point is $360^\circ$.

Therefore, the value of $x$ is 260.