Intermediate Mathematical Challenge 2025 Q20

The triangle $PQR$ is isosceles with $PQ=PR$. The point $S$ lies on the extension of the line $QR$ as shown.

$\angle RPQ=x^\circ$ and $\angle SRP=y^\circ$, where $x$, $y$ and $\displaystyle\frac{y}{x}$ are integer.

What is the largest possible value of $\displaystyle\frac{y}{x}$