notice the picture below
in a rectangle, all angles are 90 degrees and the diagonals are equal
meaning the diagonals bisect each other, they cut in equal halves
so. those two sides are equal, and thus they make up an isosceles triangle
on the sides
if those two sides are equal, the angles they make on the other side are equal
so if angle D is 55 degrees, angle A is 55 degrees
and the missing angle is 180 - (55 + 55) or 70
that's just the left-side
now, angle "x" on the right side, is a vertical angle of that angle on the left,
and vertical angles are equal, thus x = 70