2018 AMC 12A Problem 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?

\textbf{(A) } 76 \qquad \textbf{(B) } 77 \qquad \textbf{(C) } 78 \qquad \textbf{(D) } 79 \qquad \textbf{(E) } 80

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.