In Fig.,AB is parallel to CD and angle F=30*.Find ANGLE ECD.

Answer : 

We have  AB  | | CD  
And
$\angle$ AFE   = 30$°$
From figure we get 
 $\angle$ EAF  =  90$°$

In $∆$ AFE  
We know , by angle sum property of triangle 

$\angle$ AFE  + $\angle$ EAF  +  $\angle$ AEF   =  180$°$

30$°$  +  90$°$  + $\angle$ AEF  =  180$°$

 $\angle$ AEF  =  60$°$

And $\angle$ AEF   and  $\angle$ FEB are supplementary angles , So

 $\angle$ AEF  +  $\angle$ FEB  =  180$°$ 

60$°$  + ​ $\angle$ FEB  =  180$°$ 

 $\angle$ FEB  =  120$°$ 

And As we know AB  | | CD and take line CF as transversal line , so 

$\angle$ FEB  =  ​$\angle$ ECD                                                   ( Corresponding angles  ) 

So,

$\angle$ ECD  = ​120$°$                                                        ( Ans )