You can see that angle TQV = 90 degrees
Angle RQV = 136 degrees
Angles RQV and UQV are supplementary and equal 180 degrees since they form a straight line. Therefore angle UQV = 180 - 136 = 44 degrees.
TQU + UQV = 90 degrees. Therefore, TQU = 90 - UQV.
90 - 44 = 46 degrees for angle TQU.
Answer:

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This is a great question, but it's also a very broad one. Please find and post one or two actual rational expressions, so we can get started on specifics of how to find vertical and horiz. asymptotes.
In the case of vert. asy.: Set the denom. = to 0 and solve for x. Any real x values that result indicate the location(s) of vertical asymptotes.