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°

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.