https://file.aiquickdraw.com/mathbot/file/1730497339085id5fwbvv.jpg

To solve for the measure of \( \angle XYZ \) in this problem, let's analyze the information given in the circle diagram.

### Solution:
1. **Identify the type of angle**:
   - \( \angle XYZ \) is an *inscribed angle* that intercepts the arc \( VZ \).

2. **Apply the inscribed angle theorem**:
   - The inscribed angle theorem states that an inscribed angle is half the measure of its intercepted arc. Therefore, if we know the measure of the arc \( VZ \), we can find \( \angle XYZ \).

3. **Determine the measure of arc \( VZ \)**:
   - Since \( \angle VWZ = 33^\circ \) and it is also an inscribed angle that intercepts the same arc \( VZ \), the measure of arc \( VZ \) will be twice the measure of \( \angle VWZ \).
   - So, \( \text{Measure of arc } VZ = 2 \times 33^\circ = 66^\circ \).

4. **Calculate \( \angle XYZ \)**:
   - Now, using the inscribed angle theorem again, \( \angle XYZ = \frac{1}{2} \times 66^\circ = 33^\circ \).

### Conclusion:
The measure of \( \angle XYZ \) is \( 33^\circ \).

### Answer:
The correct choice is:
**A. 33°**

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Would you like further details on the steps or have any questions?

Here are 5 additional related questions for practice:
1. How would you find the measure of an angle if it subtends a semicircle?
2. If \( \angle XYZ \) was a central angle, how would the solution change?
3. What would be the measure of \( \angle VWZ \) if arc \( VZ \) measured 100°?
4. How does the inscribed angle theorem apply to angles intercepting the same arc?
5. How do you calculate the measure of an arc using multiple inscribed angles?

**Tip:** Remember that an inscribed angle is always half the measure of its intercepted arc in a circle.

Learn how to determine the measure of an inscribed angle in a circle using the inscribed angle theorem. This problem involves finding the measure of ∠XYZ by applying the theorem to calculate half the intercepted arc. Perfect for students in Grades 9-10 studying geometry and circle theorems.

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