First, to make both triangles congruent, we should have that angle P equals angle L, so we have the following:
[tex]\begin{gathered} \measuredangle P=\measuredangle L \\ \measuredangle P=9x-18 \\ \measuredangle L=4x-17 \\ \Rightarrow9x-18=4x+17 \end{gathered}[/tex]
Solving for x we get:
[tex]\begin{gathered} 9x-18=4x+17 \\ \Rightarrow9x-4x=17+18 \\ \Rightarrow5x=35 \\ \Rightarrow x=\frac{35}{5}=7 \\ x=7 \end{gathered}[/tex]
