https://file.aiquickdraw.com/mathbot/file/1725311888664cvyvtvtj.jpg

To solve question 32, let's analyze the problem shown in the image.

### Question 32: WXYZ is a parallelogram. Calculate ∠Z.

Given that WXYZ is a parallelogram, there are some key properties we can use:
1. Opposite angles in a parallelogram are equal.
2. Adjacent angles in a parallelogram are supplementary (they add up to 180°).

Let's denote the angles as follows:
- ∠W
- ∠X
- ∠Y
- ∠Z

Since opposite angles are equal:
- ∠W = ∠Y
- ∠X = ∠Z

Given that adjacent angles are supplementary:
- ∠W + ∠X = 180°
- ∠X + ∠Y = 180°

Since ∠X + ∠Z = 180° (because ∠X and ∠Z are adjacent angles), we can calculate ∠Z if we know the value of ∠X.

If we know one angle, the opposite angle can be easily calculated using the properties mentioned above. Unfortunately, the image does not provide the values directly. But the method would be:

1. Identify the given angle (if provided).
2. Use the relationship \( \text{Angle X} + \text{Angle Z} = 180^\circ \) to find ∠Z.

If you provide the specific value of any angle, I can calculate ∠Z for you. Otherwise, this is the general method to solve such problems. 

Would you like to provide any specific angle values, or is there any additional detail that you want to explore regarding parallelograms?

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### Relative Questions:
1. What is the relationship between adjacent angles in any parallelogram?
2. How do you calculate an unknown angle in a parallelogram if one angle is provided?
3. What are the properties of a parallelogram that make solving angles easier?
4. How do the properties of a parallelogram differ from those of a rectangle?
5. What methods are used to verify if a quadrilateral is a parallelogram based on its angles?

### Tip:
Always remember that in a parallelogram, both opposite sides are equal and parallel, which significantly helps in solving related angle and side problems.

Learn how to calculate angle Z in parallelogram WXYZ using properties of parallelograms. Understand the relationships between adjacent and opposite angles in parallelograms. Suitable for high school students learning geometry.

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