Pentagon with Adjustable Angles

This pentagon has images that tessellate by two rotations side to side and a midpoint rotation on the fifth side. But the angles of the side to side rotations are adjustable. The shape won't tessellate for any angles, but there are angles that do work.

Which angles work and why?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Posted at mathhombre.blogspot.com.

John Golden, Created with GeoGebra