In the diagram below, lines \( AB \) and \( CD \) are parallel, and \( EF \) intersects them at points \( G \) and \( H \), respectively. If \( \angle AGH = 70^\circ \) and \( \angle GHE = 40^\circ \), find \( \angle EGH \).
[asy]
size(6cm);
pair A = (-2,2);
pair B = (2,2);
pair C = (-2,-2);
pair D = (2,-2);
pair E = (-3,0);
pair F = (3,0);
pair G = intersectionpoint((E--F),(A--B));
pair H = intersectionpoint((E--F),(C--D));
draw(A--B);
draw(C--D);
draw(E--F);
label("$A$", A, NW);
label("$B$", B, NE);
label("$C$", C, SW);
label("$D$", D, SE);
label("$E$", E, W);
label("$F$", F, E);
label("$G$", G, N);
label("$H$", H, S);
label("$70^\circ$", G, N, blue);
label("$40^\circ$", H, S, blue);
\end{asy] Let's think step by step and output the final answer within \boxed{}.
user