jmc

Since $\overline{GA}$ and $\overline{PN}$ are diameters, point $O$ is the center of the circle. We have $\angle AON=\angle GOP=78^{\circ }$, so arc $AN$ has measure $78^{\circ }$. Since $\angle NGA$ is inscribed in arc $AN$, we have $\angle NGA=\frac{1}{2}\cdot 78^{\circ }=\boxed{39^{\circ }}$.