Question

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Answer 1

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

`2(7x-13)+2(4x-5)=360\implies14x-26+8x-10=360`

`\implies22x-36=360`

`\implies22x=396`

`\implies x=18`

Angle S (or PSR) is congruent to angle Q (or PQR) so they have the same measure:

`m\angle PSR=(7x-13)^\circ=113^\circ`