The lines $\overleftrightarrow{ab}$ and $\overleftrightarrow{cd}$ are parallel. If $\angle bae=54^{\circ}$ and $\angle dce=25^{\circ}$, what is the measure of $\angle aec$? [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].