In rectangle $EFGH$, $EH = 3$ and $EF = 4$. Let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$ and $\angle MHX = 72^\circ$, as shown below. Find $\angle XGH$, in degrees. [asy] unitsize(1 cm); pair A, B, C, D, M, X; A = (0,3); B = (4,3); C = (4,0); D = (0,0); M = (A + B)/2; X = rotate(26,M)*(D); draw(A--B--C--D--cycle); draw(D--M--X--cycle); draw(C--X); label("$E$", A, NW); label("$F$", B, NE); label("$G$", C, SE); label("$H$", D, SW); label("$M$", M, N); label("$X$", X, S); [/asy]