4) The key here is recognizing that the diagonals of a rectangle are congruent, and that they bisect each other. Therefore, AE = BE, and AE + BE = BD. Substituting, you get 
.
BD=x+7
5) The sides of a rectangle are parallel to each other. When you draw lines extending the sides, the implications of this become obvious. Suddenly, you have two parallel lines intersected by a transversal, and you probably know those angle relationships. BAC = ACD, so
. 
.
To find AED (I believe there's an easier way, but I'm not sure), see that AED is the supplement of AEB, and AEB is 180°
. Therefore, AED is 
.
AED=52°
BD=x+7
5) The sides of a rectangle are parallel to each other. When you draw lines extending the sides, the implications of this become obvious. Suddenly, you have two parallel lines intersected by a transversal, and you probably know those angle relationships. BAC = ACD, so
To find AED (I believe there's an easier way, but I'm not sure), see that AED is the supplement of AEB, and AEB is 180°
AED=52°