The value of the missing angles x and y are 37° and 53° respectively.
From the diagram given ;
The length of the chords AD and BC are parallel to each other.
The sum of opposite sides of a cyclic quadrilateral is 180. Since AD and BC are congruent.
BAD + BCD = 180
2(BAD) = 180
BAD = 180/2
BAD = 90°
BAD = 37 + y
90 = 37 + y
y = 90 - 37
y = 53°
Hence, x = 37° and y = 53°