Answer: y = 50
============================================================
Step-by-step explanation:
For any kite, the adjacent sides are congruent.
This leads to AB = BC and AD = DC
Using the SSS congruence rule, we can prove triangle ABD is congruent to triangle CBD.
From that we can say
Angle ABD = Angle CBD
as these angles correspond to one another.
----------------------
So this means angle ABD is y
Let E be the intersection point of the diagonals. Angle AEB is x = 90 as you found earlier. The diagonals of any kite are always perpendicular.
Focus on triangle AEB
The three angles of any triangle add to 180
A+E+B = 180
40+x+y = 180
40+90+y = 180
130+y = 180
y = 180-130
y = 50