In any convex quadrilateral, the sum of the interior angles' measures is 360 degrees. PQRS is a parallelogram, so angles opposite one another are congruent. This means angles Q and S are congruent, and P and R are congruent.
We have
[tex]2(7x-13)+2(4x-5)=360\implies14x-26+8x-10=360[/tex]
[tex]\implies22x-36=360[/tex]
[tex]\implies22x=396[/tex]
[tex]\implies x=18[/tex]
Angle S (or PSR) is congruent to angle Q (or PQR) so they have the same measure:
[tex]m\angle PSR=(7x-13)^\circ=113^\circ[/tex]
