Find angle in this quadrilateral

Question

In the figure below, how can we find $x$ by geometrical arguments and without using sine-cosine formulae or co-ordinate geometry. And if it is not possible solely by geometrical arguments, then why is it not possible?

Figure

Note: Image not subject to scale. Numbers are for example purpose only, one can have any other numbers as well.

Answer 1

I think the correct answer is $80^\circ$

I did it by geometrical construction.