How difficult can it be?

I really enjoy logical and mathematical problems, so when I came across the “world’s hardest easy geometry problem” I was quite excited. I mean, how difficult can it be, right? 180 degree in a triangle and you are set.

I dare anyone to try and solve the problem below: find the angle . Sure you can measure the angle, but that is cheating. Grab pen and paper and let me see your “proof”; I would be very interested in comparing notes. I spend many hours for many days solving this, but then again, I’m not the sharpest knife in the draw.

Update: I forgot to write, that you are only allowed to use simple geometry. No trigonometry is allowed.