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In this problem, we are tasked with finding the values of \( x \), \( y \), and \( z \) for the angles given in a parallelogram. In any parallelogram, the following properties are important:

1. Opposite angles are equal.
2. Adjacent angles are supplementary (they add up to \(180^\circ\)).

### Given Angles:
- \( 114^\circ \) is one angle.
- \( (5y - 9)^\circ \) is its opposite angle.
- \( (-z - 5)^\circ \) and \( (-x - 7)^\circ \) are two adjacent angles.

### Steps:
1. **Opposite Angles**: 
   - Since opposite angles are equal, we can set:
     \[
     114 = 5y - 9
     \]
     Solving for \( y \):
     \[
     5y = 114 + 9 = 123
     \]
     \[
     y = \frac{123}{5} = 24.6
     \]

2. **Supplementary Angles**: 
   - Adjacent angles sum to \(180^\circ\). So, we can set up the following equation for the adjacent angle to \(114^\circ\):
     \[
     (-z - 5) + 114 = 180
     \]
     Solving for \( z \):
     \[
     -z - 5 = 180 - 114 = 66
     \]
     \[
     -z = 66 + 5 = 71
     \]
     \[
     z = -71
     \]

3. **Opposite Angles Again**: 
   - Since opposite angles are equal, the angle \( (-x - 7)^\circ \) is equal to the previously calculated angle \( (-z - 5)^\circ \), so:
     \[
     -x - 7 = -z - 5
     \]
     Substituting \( z = -71 \):
     \[
     -x - 7 = -(-71) - 5 = 71 - 5 = 66
     \]
     Solving for \( x \):
     \[
     -x = 66 + 7 = 73
     \]
     \[
     x = -73
     \]

### Final Values:
- \( x = -73 \)
- \( y = 24.6 \)
- \( z = -71 \)

Let me know if you'd like further details or explanations! Here are 5 related questions to deepen your understanding:

1. How can you verify that a shape is a parallelogram using its angle properties?
2. What are the other angle properties of quadrilaterals besides parallelograms?
3. How do diagonals behave in a parallelogram in relation to angles?
4. Could you solve for \( x \), \( y \), and \( z \) using a different method?
5. What are the properties of rhombuses or rectangles compared to general parallelograms?

**Tip:** Always double-check if a shape satisfies the basic properties of geometric figures (e.g., opposite angles in a parallelogram) before solving.

Find the value of x, y, and z in the parallelogram shown in the image, where the angles provided are (5y - 9)°, (-x - 7)°, (-z - 5)°, and 114°.

Learn how to solve for x, y, and z in a parallelogram where angles are expressed algebraically. This problem involves the properties of opposite and adjacent angles, utilizing both the Opposite Angle Theorem and the Supplementary Angle Theorem.

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