Let $M$ and $N$ be the midpoints of sides $C D$ and $D E$ of a regular hexagon $A B C D E F$. Find the angle between the lines $A M$ and $B N$.

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When rotating by $60^{\circ}$ around the center $X$ of the regular hexagon $A B C D E F$, which maps vertex $A$ to vertex $B$, vertex $C$ transitions to vertex $D$, and vertex $D$ transitions to vertex $E$. Therefore, the midpoint $M$ of segment $C D$ transitions to the midpoint $N$ of segment $E D$, and the line $A M$ transitions to the line $B N$. Consequently, the desired angle is $60^{\circ}$.

## Answer

$60^{\circ}$.