Example 4 As shown in Figure 4, in rhombus $A B C D$, $\angle A B C$ $=120^{\circ}, F$ is the midpoint of $D C$, and the extension of $A F$ intersects the extension of $B C$ at point $E$. Then the degree measure of the acute angle formed by line $B F$ and $D E$ is ( ).
(A) $30^{\circ}$
(B) $40^{\circ}$
(C) $50^{\circ}$
(D) $60^{\circ}$
(2008, National Junior High School Mathematics League Wuhan CASIO Cup Selection Competition)
As shown in Figure 4, let $B F$ intersect $D E$ at point $M$, and connect $B D$. Then $\triangle B C D$ is an equilateral triangle.
From $F$ being the midpoint of $C D$, we know $\angle M B C=30^{\circ}$.
Since $A D / / C E$, then $\triangle A D F$ and $\triangle E C F$ are centrally symmetric about point
$F$. Therefore, $C E=A D=C D$.
Thus, $\angle C E M=30^{\circ}, \angle D M F=60^{\circ}$.