If $\widehat{PQR}=\widehat{QRS}=\alpha$ then $\widehat{QPS}=\widehat{RSP}=180-\alpha$
Then $\widehat{QRS}+\widehat{RSP}=180\Rightarrow QR\parallel PS$ and the quadrilater is an isosceles trapezoid. Then $PQ=RS$.
But $PQ=9, \ RS=4$.