How smart is /b?

agreed with germanon here that this is fishy
checked for x=30 on geogebra though

This is where I got stuck. I think there may be no solution

Umm, you mean 40, not 140

50 because of a reflection, and the straight line is 180 minus 50. Then split in two. Then reflection of 65 is also 65.

as said x=30 is the solution but I could only verify it

Oh shit typo.

I dont know. I think there should be a solution. If you vary the angle x then the top left corner would also change its position and the angles in the left triangle would change.
So intuitively I would assume there is only one angle x which fulfills that constellation. But I cant figure out how to calculate it.

How do you know the line is split evenly?
Would measuring these lines do anything?

The rhombus still adds up to 390 degrees so it's wrong

No where in the op image does it imply that the line where you "split in two" actually splits the angle into two equal angles.