The Nineteenth Hole

How can I prove that the angles of a five pointed star add up to 180 degrees (inside pentagon is not regular)?

I want to prove that the end tips of a five pointed star add up to 180 degrees. It's easy to do when the pentagon inside is a regular polygon, but what if it's not? AHHH!!!! I'm getting really frustrated trying to find a way to prove it. HELP ME!!

It really doesn't matter if it is regular. Draw the "star" by drawing all of the diagonals of the pentagon. Note that inside the star is another pentagon. You know the sum of all the angles of this (or any polygon) is just (n-2)*180 or for you, (5-2)*180 = 540. There are lots of triangles now that you can use with these angles and the "tips" to get the job done.

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