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_/]

Solve all the obvious angles, you'll be left with four (all in the upper sort of area). After applying one simple fact, you're left with four "a+b=something" formulae, four variables, and just solve.

(okay, I admit that I made an intelligent guess at that point rather than solving them, but I got a correct answer... and it should be solvable via algebra. I'm just lazy.)

[giddysinger.livejournal.com]

That doesn't quite work. Everything ultimately reduces down to "the sum of angles AED and BDE equals 130." The solution is going to require more than the "sum of the angles" trick.

(Not saying that either the wife or I have solved it, but still...)

[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°).