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In the given parallelogram, we need to find the values of angles \( x \), \( y \), and \( z \). Here's how we approach this problem:

### Key Properties of a Parallelogram:
1. Opposite angles of a parallelogram are equal.
2. Adjacent angles in a parallelogram are supplementary (they add up to \( 180^\circ \)).

### Solution Steps:
- The angle labeled \( 88^\circ \) is an adjacent angle to \( z^\circ \), and since adjacent angles in a parallelogram are supplementary:
  \[
  z = 180^\circ - 88^\circ = 92^\circ
  \]

- Opposite angles are equal in a parallelogram. Therefore:
  \[
  x = z = 92^\circ
  \]

- Since \( y \) is opposite to the \( 88^\circ \) angle, we know:
  \[
  y = 88^\circ
  \]

### Final Values:
- \( x = 92^\circ \)
- \( y = 88^\circ \)
- \( z = 92^\circ \)

Would you like further details on this solution or any related concepts?

Here are some related questions for practice:
1. What is the sum of all interior angles in any parallelogram?
2. Can a parallelogram have right angles?
3. How do you find the area of a parallelogram?
4. What is the difference between a rhombus and a parallelogram?
5. How do diagonals behave in a parallelogram?

**Tip:** Remember, in any parallelogram, opposite angles are always equal, and adjacent angles are supplementary.

Find the values of x, y, and z in the parallelogram with angles 88°, x°, y°, and z°.

Learn how to find the missing angles x, y, and z in a parallelogram with one given angle of 88°. This problem covers key geometric concepts and the properties of parallelogram angles, suitable for students in Grades 6-8.

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