The measure of ZEFH is twice the measure of ZGFH. What is the degree measure of ZGFH?

I like the word "precise name", because two answers fit the bill.

One (square) will fit the bill but less general.
The other (rhombus) will fit the bill and INCLUDE all cases of squares, since a square is a rhombus!

Reasoning:
A rhombus or a square both have all four sides equal.
Diagonals intersect each other at 90 degrees.  
As well, diagonals divide figure into two congruent isosceles triangles, hence bisects the angles at the vertices.