Creation of this applet was inspired by the [url=http://www.puzzles.com/puzzleplayground/RaysThroughTheSquares/RaysThroughTheSquares.htm]Rays Through the Squares problem after Martin Gardner[/url]. [br][br]1) Can you prove, using only elementary geometry (and no trigonometry), [br] that the [color=#ff00ff][b]pink angle measure[/b][/color] equals the sum of the measures of the [color=#38761d][b]green[/b][/color] and [color=#ff7700][b]orange[/b][/color] angles? [br][br]2) Can you create some new trigonometric (or even better--"inverse trigonometric") identities[br] based upon your observations?