Lets fill in what we can as we go and work our way around to find all the angles and make sure they add to the correct degree.
Lets begin with the supplementary angle next to 142 at the--bottom right and that triangle
180-142=38
180-38-49=93
w=93
Moving to the triangle above that one
vertical angles are congruent
w=93, so the angle above it is 93
180-93-42=45
Now the very bottom triangle
180-142=38
180-38-73=69
To move any further we need to find the angles of the hexagon in the center(hexagon interior angles=720)
180-93=87(93 is w)
(left of 142)180-69=111
(right of 131)180-45=135
131+135+87+142+111=606
180-606=114
z=114
Upperleft triangle
y=180-131
y=49
180-114=66(114 is z)
x=180-49-66
x=65
Bottom left triangle
180-114=66
180-111=69
180-66-69=45
Answer: z=114
Hope this helps, I know I went into unecessary detail :)
