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

Step 1: Identify the given information and the goal. 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 $C$.

Step 2: Calculate the interior angle at $D$. The sum of angles around a point is $360^\circ$. The interior angle at $D$, $\angle CDE$, is given by: $\angle CDE = 360^\circ - 312^\circ = 48^\circ$

Step 3: Draw an auxiliary line through point $C$ parallel to $BA$ and $DE$. Let's draw a line $FCH$ passing through $C$, such that $FCH \parallel BA$ and $FCH \parallel DE$.

Step 4: Use the property of alternate interior angles for $BA \parallel FCH$. Considering $BC$ as a transversal cutting parallel lines $BA$ and $FCH$: $\angle BCF = \angle ABC$ Since $\angle ABC = 52^\circ$, we have: $\angle BCF = 52^\circ$

Step 5: Use the property of alternate interior angles for $FCH \parallel DE$. Considering $CD$ as a transversal cutting parallel lines $FCH$ and $DE$: $\angle DCH = \angle CDE$ Since $\angle CDE = 48^\circ$, we have: $\angle DCH = 48^\circ$

Step 6: Calculate the interior angle $\angle BCD$. From the diagram, the interior angle $\angle BCD$ is the sum of $\angle BCF$ and $\angle DCH$: $\angle BCD = \angle BCF + \angle DCH$ $\angle BCD = 52^\circ + 48^\circ = 100^\circ$

Step 7: Calculate the reflex angle $x^\circ$. The angle $x^\circ$ is the reflex angle at $C$. The sum of angles around a point is $360^\circ$. $x^\circ = 360^\circ - \angle BCD$ $x^\circ = 360^\circ - 100^\circ = 260^\circ$ Therefore, the value of $x$ is $260$.

The final answer is $\boxed{260}$.