Question 1
In triangle $ABC$, $\angle A=60^\circ$. Points $D,M$ lie on the line $AC$, and points $E,N$ lie on the line $AB$, such that $DN$ and $EM$ are the perpendicular bisectors of $AC$ and $AB$, respectively. Let $L$ be the midpoint of $MN$. Prove that $\angle EDL=\angle ELD$.