Star Problem

What is the sum of the measures of the angles of a star? Play with the figure below and answer the questions that follow.

What does n tell us about the diagram?

What does i tell us about the diagram?

What does the gold slider do?

How can you compute the sum of the angles at the marked vertices? (Heavy spoilers here.)

Want to learn more? Here are two ideas. 1) Download the GeoGebra file associated with this activity. Go into the properties on slider . You'll notice that it currently ranges from to . Change the upper bound to , close the properties dialog, and see what weirdness ensues. 2) Check out a related video by Mathologer, called The 3-4-7 Miracle.