First one
When two lines intersect, vertical angles are formed. If two angles are vertical, they are congruent; in other words, they have the same measure.
Thus, as we can see, x and z are vertical angles.
Second one
Same side interior angles are angles that are on the same side of the transversal and are between the other two lines. Graphically,
Thus, as we can see, z and w are same-side interior angles.
Third one
Supplementary angles are two angles whose sum is 180 degrees. Graphically,
Thus, as we can see, w and y are supplementary angles.
Fourth
Corresponding angles are angles that have the same relative position i
