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Star Polygons

Age 11 to 14 Challenge Level:
Here is a five-pointed star:
  
Draw a couple of five pointed stars of your own, making sure your lines are nice and straight!
Measure the interior angles at the five points and add them together.

What do you notice? Can you prove it?


Here is a seven-pointed star:

 

Draw some seven-pointed stars of your own.
Measure the interior angles at the seven points and add them together.

What do you notice? Can you prove it?



You might find the animation below helpful:





Click below to reveal a picture from the end of the animation:
 



Can you state and prove similar results for any different types of stars?