In the figure, if the measure of arc $FG$ is $118^\circ$, the measure of arc $FQ$ is $25^\circ$, and $FR = FG,$ then what is $\angle RPG$, in degrees?

[asy]
unitsize(2 cm);

pair K, M, P, Q, R;

K = dir(220);
M = dir(-20);
Q = dir(20);
R = dir(110);
P = extension(K,Q,M,R);

draw(Circle((0,0),1));
draw(R--M--K--Q);

label("$G$", K, SW);
label("$F$", M, E);
label("$P$", P, N + (0,1));
label("$Q$", Q, E);
label("$R$", R, NW);
[/asy]