Hi @rbergerIBD,
Regarding this: "Assuming I do put the two dimensions on the left side, I don't understand why I need to add a dimension to the right side since I set the constraint that the line segment between the fillets should be equal to both sides. In fact even though they are have the equal constraint, they are equal length." The reason why the dimension is needed on the right side is because the Equal constraint only says that the two lines must be equal in length. It does not say that they have to be at the same angle. Adding the two dimensions on the left fixes the angle of the line. Then, because the line on the right is constrained to be equal length, you only need one of the dimensions to fully constrain it.
Regarding this question: "But what are the two dimensions you drew that are "at an angle" to the line? I can make them happen but I'm not clear what they are properties of and how I can constrain them between the two sides", those are horizontal and vertical dimensions. The essentially specify the distance in either the X or Y directions between the two endpoints of the line. You could also have done this another way by adding an Aligned dimension (which specifies the length of the line), plus an angle dimension (which specifies the angle to a fully-constrained line):

As to how to make it so that you can change only the left side dimensions, and have the whole sketch update, I would just set the dimension on the right to be based on the one on the left:
You can also use Symmetry constraint or mirror, but given that you are close already, I would go with the dimension equation instead
Jeff Strater
Engineering Director