I think that the Z that appears typed in this question is in fact the symbol for angle.
Assuming that we are taking about angle PQR (which measures 119 degrees) and which is bisected by the segment QS, here is the answer:
The bisection of an angle divides the angle in question in two angles of the same measure. So the angles formed in the bisection must be equal, and added give back the original angle.
That is:
If angle PQR is 119 degrees, then it is bisected in two equal angles :
PQS and RQS both of the same measure: 119/2 = 59.5 degrees.
So measure of PQS = 59.5 degrees
and measure of RQS = 59.5 degrees