An Isosceles Mystery

Topic:
Angles
David Marain (http://mathnotations.blogspot.com/, @dmarain) shared an angle chasing puzzle in the 80-80-20 isosceles triangle. Quite a nice one. I chased a bit, then modeled in GeoGebra. Then I made a tool for making an ASA triangle which was handy for making angle chasing problems. Then I generalized the problem, and found that the 80-80-20 triangle had lots of neat situations that other triangles do not. Is there something that makes this triangle special? Tumblr post with several examples: http://mathhombre.tumblr.com/post/92497963079/david-marain-dmarain-shared-an-angle-chasing
More GeoGebra at bit.ly/mh-ggb