Regular Decagon Magic!

Can you find evidence of the [b]golden ratio[/b] anywhere in this animation? If so, where? Explain. [br][br]What is the measure of the [b][color=#ff00ff]pink angle[/color][/b]? How do you know this to be true?[br][br]See any [b][color=#38761d]Golden Triangles[/color][/b]? See any [b][color=#bf9000]Golden Gnomons[/color][/b]? [br][br]What is the exact value of the ratio of the [b][color=#980000]brown segment[/color][/b] to the [b]segment with 3 hash marks[/b]? [br][br][b][color=#0000ff]How can we formally prove any of the phenomena dynamically illustrated here? [br][/color][/b]
Quick (Silent) Demo

Information: Regular Decagon Magic!