I believe you've given enough information to solve the whole figure in the geometry problem.

Given that the medial triangle is congruent with the other three sub triangles formed, XY = LZ = ZK. If the length of ZK is known to be 8, then triangle KYZ can be solved because the givens are two sides and the included angle.

Once triangle KYZ is solved, you can use congruence relationships to know any other side or angle measure in the figure.

If I'm right all of the answers can be determined and are as follows.

A) is 16
B) is 67 degrees
C) is 14
D) is about 78.894 degrees, or more precisely acos((8^2 + ((14^2) + (8^2) − (2×14×8×cos(67))) − (14^2))÷(2×8×( √((14^2) + (8^2) − (2×14×8×cos(67)))))) degrees

Looking back on this, I'd probably guess you were looking for answer D.