Find the lengths of bc and xz and the measure of bzx

BC = 12; XZ = 8; BZX = 55

To find BC:
Since XY is the bisector of AB and AC, this means that it is a median of triangle ABC.  Its length will be half of the length of BC; 6 = 1/2BC; 6*2 = BC; 12 = BC

To find XZ:
Since XZ is the bisector of AB and BC, this means that it is a median of triangle ABC.  Its length will be half of the length of AC; 1/2(16) = 8.

To find BZX:

XYCZ is a parallelogram.  Consecutive angles of a parallelogram are supplementary; 180-55=125=XZC.

XZC and BZX form a linear pair and are thus supplementary.  This means that BZX = 180-XZC = 180-125 = 55