check the picture below.
the kite, is a quadrilateral, 4 sides, and all interior angles in a polygon is 180(n-2) where n = sides, so 180(4-2) is 360° total.
since in a kite, one pair of angles are congruent, namely the ones at A and C, then we can get D by getting the slack from 360° and the other angles, as you see in the picture.
since the diagonal is an angle bisector to D as well as B, ∡ADE is half of ∡D.
