Answer:
(D)
Step-by-step explanation:
It is given that Kite WXYZ has a short diagonal of XZ and a long diagonal of WY. The diagonals intersect at point V. The length of XZ = 8cm, and the measure of ∠XYV is 30°.
We know that the diagonals are the perpendicular bisectors of each other, therefore
⇒
.
Now, from ΔVXY using trigonometry, we get

Substituting the given values, we get


Therefore, the length of the segment VY is
.
Hence, option D is correct.