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Math·Geometry and Trigonometry·Lines, angles, and triangles

hard

In triangle $PQR$, the measure of angle $P$ is $(3x+5{)}^{\circ }$, the measure of angle $Q$ is $(2x+9{)}^{\circ }$, and the measure of angle $R$ is $(4y+5{)}^{\circ }$. If side $QR$ is extended through point $R$ to point $S$, and the measure of angle $PRS$ is $9y^{\circ }$, what is the value of $x+y$?

1

34.89