In $△PAT$, $\angle P=20^{\circ }$, $\angle A=80^{\circ }$, and $PA=8$. Points $U$ and $G$ lie on sides $\overline{TP}$ and $\overline{TA}$, respectively, so that $PU=AG=1$. Let $M$ and $N$ be the midpoints of segments $\overline{PA}$ and $\overline{UG}$, respectively. What is the degree measure of the acute angle formed by lines $MN$ and $PA$?