Since a kite has one pair of opposite angles which are congruent, W and Y must be congruent because X and Z are not.
The sum of the angles in any quadrilateral is 360 degrees. We know two of the angles as 90 degrees and 40 degrees, so the sum of the other two angles must be 360-90-40 = 230 degrees.
We know that W and Y must be equal so each of them is equal to 230/2 degrees = 115 degrees.
