The lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel. If $\angle BAE=54^{\circ}$ and $\angle DCE=25^{\circ}$, what is the measure of $\angle AEC$?

Use an asymptote convertor if needed:

[asy]
size( 200 ) ;

pair A = (0,0) ;
pair B = (0,2) ;
pair C = (3,0.5) ;
pair D = (3,2.5) ;
pair ptE = extension( A , A+dir(90-54) , C , C+dir(90+25) ) ;

draw( (0,-0.5)--(0,3) , linewidth(1.3) ) ;
draw( (3,-0.5)--(3,3) , linewidth(1.3) ) ;
draw( A--ptE--C ) ;
dot(Label( "$A$" , A , W )) ;
dot(Label( "$B$" , B , W )) ;
dot(Label( "$C$" , C , E )) ;
dot(Label( "$D$" , D , E )) ;
dot(Label( "$E$" , ptE , N )) ;

label( "$54^{\circ}$" , A , 5dir(70) ) ;
label( "$25^{\circ}$" , C , 8dir(100) ) ;
[/asy]