Kite Tessellation by 2 Side-to-side Rotations

This sketch allows you to control the angle between the congruent sides on a kite. That way, you can experiment to see for what angles does this tessellation pattern work.

1) Find some different kites that tessellate with two rotations. Record the angles in the kite.
2) What are the values for a and b that make the kite into a different geometric shape?
3) Since the kites always fit together around 2 vertices, what makes the difference for when they tessellate or not?
4) Can you use algebra to find all the kites that tessellate with two rotations?

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John Golden, Created with GeoGebra