<p>Revisting post #6.
We are free assume that that perpendicular from the point D passes through the point A (it won’t change the answer); that makes ABDC a rhombus, therefore y=x/2.</p>
<p>=============
When plugging numbers, all the manipulations are the same as in strictly math method, but are easier to follow.
Let x=80, then
<ABC = 50,
<BCD = <ABC = 50 as alternate interior angles,
y = 90 - 50
y=40.
Only answer D satisfies x=80 and y=40.</p>