help geometry

This is impossible

If   AB  and CD are parallel, then angles   AXE and CYX are equal  since they are corresponding  angles

You are missing angle measures. There is no way to solve it without more. Following my knowledge of proofs and just proving angles in a nutshell there is no way to do this....

If you can give us more angle measures I'll be more than happy to help! 

ILP

I think it is possible...

Let $\angle AXE = \angle CYX = x$

We have the equation: $x = 3x-98$

Solving for x, we find that $x = 49$.

Now we have: $\angle AXE = \angle BXY = \color{brown}\boxed{49}$

What am I missing?