Cut-The-Knot-Action (5)!

Creation of this applet was inspired by a [url=https://twitter.com/CutTheKnotMath/status/839945580088602629]tweet[/url] from [url=https://twitter.com/CutTheKnotMath]Alexander Bogomolny[/url]. [br][br]In the applet below, a [b][color=#6aa84f]regular pentagon[/color][/b] and a [color=#bf9000][b]regular decagon[/b][/color] share a common side. [br][br][color=#ff00ff][b]What is the measure of the pink angle? [/b][/color] [br][br][color=#0000ff][b]How can you formally prove what this applet informally illustrates? [/b][/color]

Medians & Equal Areas!

[color=#000000]Recall [/color][color=#ff7700][i]if 2 triangles have equal bases and equal heights, they have equal areas.[br] [/i][/color][br][color=#000000]Since this is so, we can [i]informally[/i] conclude that[/color] [color=#0000ff][b]the 3 medians of any triangle split this triangle up into[/b][/color] [color=#ff7700][b]6 smaller triangles of equal area. [/b][/color][br][br]Feel free to move the triangle's white vertices anywhere you'd like at any time. [br][br][color=#000000]Again, this applet displays an [/color][i]informal illustration[/i][color=#000000] of this fact using transformational geometry techniques. [br][/color][i][color=#ff00ff][br]Yet how could you formally prove what this applet informally illustrates? [/color][/i]
Quick Demo (BGM: Andy Hunter)