geometry puzzle

[cellio]

You're being too productive; let me help:

World's hardest easy geometry problem, forwarded by a coworker, allegedly solvable with pure geometry (no trigonometry).

Comments

[http://users.livejournal.com/merle_/]

No? Hmm. I got it down to the four angles around the upper line segment that goes through the main triangle, and from there found a solution.

I do admit to looking at the equations, thinking "this feels right", and just trying a number for one of those four angles.

As well as the sum of the angles in a triangle trick, you need the sum of angles coming off of a line trick (ie one line, several lines emerging from a single point on that line, the sum of those angles is 180°).