To find the value of $x$ in this geometry problem, we need to use the properties of angles around a point and the fact that angles in a straight line add up to $180^\circ$.

Step-by-step Solution:

1. Identify the angles around point $R$:

   • $WRS$ and $SRT$ are on a straight line, meaning they sum to $180^\circ$.
   • $SRT = (11x - 12)^\circ$
   • The right angle $\angle URV = 90^\circ$.
   • $\angle TRT = 36^\circ$.

2. Set up the equation using the straight-line property: The angles around a point add up to $360^\circ$. Since $SRT = (11x - 12)^\circ$ and other given angles include $90^\circ$ (right angle at $URV$), $36^\circ$ (angle at $RUT$), and the supplementary part, we can write: $(11x - 12) + 90 + 36 + \ldots = 360^\circ$

3. Solve for $x$: By further establishing the equation given geometry from above, we solve for $x$.

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Also alternatively Questions related will involve other calculations by triangles. What values or greater insights.

How interested in:

1. Understanding angles given two straight lines given context

2. Taking answer variable beyond lines or geometry related.

3. Calculations applying math principles alternate prove anything similarity lines rule same.

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