To find the unknown angles x, y, and z in Wendell's diagram, we can use the properties of angles formed by intersecting lines. Here's how to determine the measure of each angle:

- Angle x: This angle is formed by the intersection of the line parallel to side AB and the line connecting the top of the hill and the bottom of the valley. Since these lines are parallel to sides of the parallelogram, angle x can be determined using the alternate interior angles property. The alternative interior angle to angle x is known to be 120 degrees (provided in diagram). Therefore:

>> Angle x = 120 degrees

- Angle y: This angle is formed by the intersection of the line connecting the left side of the hill and the bottom of the valley and the line connecting the top of the hill and the bottom of the valley. We can see that angle y is opposite to angle x in the parallelogram, and opposite angles in a parallelogram are congruent. Therefore:

>> Angle y = 120 degrees

- Angle z: This angle is formed by the intersection of the line parallel to side CD and the line connecting the top of the hill and the bottom of the valley. Like angle x, angle z can be found using alternate interior angles:

>> Angle z = 120 degrees

So, we have found that:

Angle x = 120 degrees

Angle y = 120 degrees

Angle z = 120 degrees