Question 23
In $\triangle PAT,$ $\angle P = 36^\circ,$ $\angle A = 56^\circ,$ and $PA = 10.$ 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 $PA?$