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The problem involves finding the values of \( x \), \( y \), and \( z \) in a parallelogram \( ABCD \) with given angles and side lengths. Here's a detailed solution:

### Problem Analysis
- The figure shows a parallelogram \( ABCD \).
- \( \angle DAB = 70^\circ \) and \( \angle ABC = 102^\circ \).
- The side lengths are given as \( AB = (2x - 1) \) cm, \( BC = (2y + 2) \) cm, and \( CD = (2z + 3) \) cm.

### Properties of Parallelogram:
1. **Opposite Angles are Equal**: 
   - \( \angle DAB = \angle BCD = 70^\circ \).
   - \( \angle ABC = \angle CDA = 102^\circ \).

2. **Consecutive Angles are Supplementary**:
   - \( \angle DAB + \angle ABC = 180^\circ \).
   - This is already given, so it confirms the angles provided are consistent with the properties of a parallelogram.

3. **Opposite Sides are Equal**:
   - \( AB = CD \) and \( BC = DA \).

### Solution Steps:
#### 1. Set Up the Equations:
Using the property that opposite sides of a parallelogram are equal:
- \( AB = CD \) implies:
  \[
  2x - 1 = 2z + 3
  \]
- \( BC = DA \) implies:
  \[
  2y + 2 = BC = DA = AB = 2x - 1
  \]

#### 2. Solve the Equations:
- **From the first equation**: 
  \[
  2x - 1 = 2z + 3
  \]
  Simplify this to:
  \[
  2x - 2z = 4 \quad \text{or} \quad x - z = 2 \quad \text{(Equation 1)}
  \]

- **From the second equation**:
  \[
  2y + 2 = 2x - 1
  \]
  Simplify this to:
  \[
  2x - 2y = 3 \quad \text{or} \quad x - y = \frac{3}{2} \quad \text{(Equation 2)}
  \]

#### 3. Solve the System of Equations:
From Equation 1:
\[
x = z + 2
\]
Substitute this into Equation 2:
\[
(z + 2) - y = \frac{3}{2}
\]
Solve for \( y \):
\[
y = z + \frac{1}{2}
\]

### Summary of Values:
- \( x = z + 2 \)
- \( y = z + \frac{1}{2} \)

The values of \( x \), \( y \), and \( z \) depend on each other. Without additional specific numeric conditions, we can't determine unique values, but they follow the relationships above.

### Further Questions for Exploration:
1. How would the relationships change if the side lengths were given specific numerical values?
2. What additional information is necessary to find the exact numerical values of \( x \), \( y \), and \( z \)?
3. What are the implications if the parallelogram was not specified (e.g., if it were a rhombus or rectangle)?
4. Can you derive the area of the parallelogram given the side lengths and angles?
5. How would the problem change if angles other than 70° and 102° were given?

**Tip:** In parallelograms, opposite angles and sides are equal, and adjacent angles are supplementary—key properties that simplify solving problems like this one.

In the adjoining figure, ABCD is a parallelogram. Find the values of x, y, and z.

This problem involves finding the values of x, y, and z in a parallelogram ABCD using properties of parallelograms. Suitable for students in Grades 9-11, the solution involves applying algebraic equations derived from the geometric properties of the shape.

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