Concave Quadrilateral Craziness! (GoGeometry Action 80)

Creation of this applet was inspired by a tweet from Antonio Gutierrez (GoGeometry). The applet below contains a concave quadrilateral. (If you don't remember what the adjective concave means with respect to polygons, click here for a refresher.) You can move the BIG VERTICES of this quadrilateral anywhere you'd like. You can also control the size of the interior angle with pink vertex using the pink slider. How would you describe, in words, the phenomenon you see? How can we formally prove what is informally illustrated here?

Quick (Silent) Demo