BCD and ABD are two individual triangles here.

BCD is an isosceles triangle as BD=CD given.
Hence u =v.

ABC is a straight line. So z + v = 180 => z + u = 180. (As u = v)

Also plz let me know how z+u = 180 here.

To find x + y:

x + y = 180-z ( In Triangle ABD)
x + y = 180 - (180-v) = v

v needs to be determined to find x + y.

Given the angle of v in (1), (1) is sufficient to determine x + y.

Consider (2): w = 32.

In Triangle BCD, w + u + v = 180 => w + 2v = 180
2v = 180 - w = 180 - 32
=> 2v = 148.
=> v = 74.

v is determined and So is x+y.

(2) is sufficient to determine x + y.

Hence The answer is D.

thanks for the explanation