In the diagram below, we have $\overline{AB}\parallel\overline{CD}$ and $QP = QR$. If $\angle BPQ = 2x^\circ + 105^\circ$ and $\angle APR = 5x^\circ - 27^\circ$, then find $x$.
Hello, Wiseowl..... You need to include the diagrams to which you refer in your questions if you want to get help with them !
~EP