Since UV is a diameter, we know that m(UV) = 180 degrees. Therefore, m(VW) = 180 - m(UVW) = 180 - 202 = -22 degrees. However, angles cannot have negative measures, so we add 360 degrees to get m(VW) = 338 degrees.
Since UX is tangent at U, we know that angle U is a right angle. Therefore, m(UX) = 90 degrees. Using the fact that the sum of angles in a triangle is 180 degrees, we can find that m(VUX) = 90 - (m(UV)/2) = 90 - (180/2) = 0 degrees.
Finally, we can use the fact that angles around a point sum to 360 degrees to find m(WUX):
m(WUX) = 360 - m(UVW) - m(VUX) = 360 - 202 - 0 = <<360-202-0=158>>158 degrees.
Therefore, the bold answer is: 158 degrees.