In the following figure, AF is the perpendicular bisector of DN. What is the measure of angle ADF?

Start at F ....BOTH angles there are 90 degrees

   so for the triangle on the RIGHT   (remember all angles of a triangle add to 180 degrees?)

         the angle on the right side at A would equal   180    -    90 - 65 =  25 degrees

             AF BISECTS angle A...so both of the angles at A are equal  at   25 degrees

Now you should be able to figure the angle at D.....

 

 

Another way:

 

Both angles at A are equal       both angles at F are equal    

so the remaining angles at D and N have to be equal.....(remember all angles of a triangle add to 180 degrees?)