23. In $\triangle P A T$, $\angle P=36^{\circ}, \angle A=56^{\circ}$, $P A=10$, points $U$ and $G$ are on sides $T P$ and $T A$ respectively, with $P U=$ $A G=1$. If $M$ and $N$ are the midpoints of $P A$ and $U G$ respectively, then the acute angle formed by $M N$ and $P A$ is ( ).
(A) $76^{\circ}$
(B) $77^{\circ}$
(C) $78^{\circ}$
(D) $79^{\circ}$
(E) $80^{\circ}$
23. E.

As shown in Figure 10, extend $P N$ to point $Q$ such that $P N = N Q$, and connect $A Q$ and $G Q$.
Figure 10
Given $P N = N Q, U N = N G$
$\Rightarrow \triangle P N U \cong \triangle Q N G$
$\Rightarrow \angle U P N = \angle G Q N, Q G = P U = A G$
$\Rightarrow P U \parallel G Q$
$\Rightarrow \angle T = \angle Q G T = 2 \angle Q A T$.
In $\triangle P A T$, given $\angle P = 36^{\circ}, \angle A = 56^{\circ}$, we know $\angle T = 88^{\circ}, \angle T A Q = 44^{\circ}$.
Given $P M = M A, P N = N Q \Rightarrow M N \parallel A Q$
$$
\begin{aligned}
\Rightarrow & \angle P M N = \angle P A Q \\
& = \angle P A T + \angle T A Q = 100^{\circ} .
\end{aligned}
$$

Therefore, the acute angle formed by $M N$ and $P A$ is $80^{\circ}$.