First of all, linear pair angles are those which sum 180° in total. However, the problem states that these angles have equal measures, so each of them must be equal to 90°
[tex]5x=90,9y-45=90[/tex]Let's solve each equation.
[tex]5x=90\rightarrow x=\frac{90}{5}=18[/tex]The second result would be
[tex]9y-45=90\rightarrow9y=90+45\rightarrow9y=135\rightarrow y=\frac{135}{9}=15[/tex]