We know that \((5x + 2y - 25) + z = 180\).
Solving for z, we find that \(z = 205 - 5x - 2y\)
Using, alternate interior angles, we know that \(2y + x + y + 205 - 5x - 2y = 180\)
Simplifying, we find that \(25 = 4x - y\)
Because we want \(L_4\) to be parallel to \(L_3\), the angles must be equal, meaning: \(2y = 4x + 10 \)
We now have a system of equations to solve: \(2y = 4x +10\) and \(25 = 4x - y\)
Solving, we find \(\color{brown}\boxed{x =15, \space y = 35}\)
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