The three angles above the bottom line are supplementary, so they add up to 180° in measure:
2x° + 90° + x° = 180°
3x° + 90° = 180°
3x° = 90°
x = 30
The angles with measure x° and 2y° are congruent, since they form a pair of interior angles that alternate with respect to the transversal (in this case, this is the ray that starts from the bottom line and point up and to the right, and passes through the parallel upper line). So
2y° = x°
2y° = 30°
y = 15
Below the upper line, the two angles 2y° and z° are supplementary, so
2y° + z° = 180°
30° + z° = 180°
z = 150
