Rhombus Surprise! (GoGeometry Action 57)

Creation of this applet was inspired by a [url=http://www.gogeometry.com/education/p455_rhombus_inscribed_circle_angle_45_degrees.htm]post[/url] from Antonio Gutierrez ([url=http://www.gogeometry.com/]GoGeometry[/url]). [br][br][color=#ff00ff][b]What is the measure of the pink angle? [/b][/color] [br][br][b][color=#0000ff]How can we formally prove what is informally illustrated here? [/color][/b]
Quick (Silent) Demo

Information: Rhombus Surprise! (GoGeometry Action 57)