Angles XWY and VWY are supplementary, so the angle measure of XWY is (180 - 6x)°.
Similarly, angles XYW and ZYW are also supplementary, so the measure of XYW is (180 - 4x)°.
The interior angles of any triangle sum to 180°. Triangle XYW is a right triangle, so we have
(180 - 6x)° + (180 - 4x)° + 90° = 180°
Solve for x :
(180 - 6x) + (180 - 4x) + 90 = 180
450 - 10x = 180
270 = 10x
x = 27