Points $D$ and $N$ on the sides $AB$ and $BC$ and points $E,M$ on the side $AC$ of an equilateral triangle $ABC$, respectively, with $E$ between $A$ and $M$, satisfy $AD+AE=CN+CM=BD+BN+EM$. Determine the angle between the lines $DM$ and $EN$.
Source: Moldova 2000 Grade 7 P8
Tags: geometry, Triangle
Points $D$ and $N$ on the sides $AB$ and $BC$ and points $E,M$ on the side $AC$ of an equilateral triangle $ABC$, respectively, with $E$ between $A$ and $M$, satisfy $AD+AE=CN+CM=BD+BN+EM$. Determine the angle between the lines $DM$ and $EN$.