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The problem involves an inscribed angle \( \angle Y \) in a circle, subtended by arc \( XZ \). You are asked to find the measure of arc \( XZ \) given that \( \angle Y = 60^\circ \).

### Key Concept:
- **Inscribed Angle Theorem**: An angle inscribed in a circle is half the measure of the arc it subtends. That is, if an angle \( \theta \) subtends an arc, the arc will measure \( 2\theta \).

Given:
- \( \angle Y = 60^\circ \)

Using the inscribed angle theorem:
\[
\text{Measure of arc } XZ = 2 \times \angle Y = 2 \times 60^\circ = 120^\circ
\]

### Answer: 
The measure of arc \( XZ \) is \( 120^\circ \), which corresponds to option **A**.

Would you like more details or have any further questions?

Here are some related questions for practice:
1. What is the measure of the arc opposite to \( XZ \) (arc \( ZYX \))?
2. If \( \angle ZXY = 30^\circ \), what is the measure of the arc \( ZY \)?
3. How does the measure of the central angle compare to the inscribed angle subtended by the same arc?
4. If the radius of the circle is 5 units, what is the length of arc \( XZ \)?
5. How would the answer change if \( \angle Y \) were 45° instead of 60°?

### Tip:
Always remember, an inscribed angle is half the measure of the arc it subtends, which is useful in many circle-related problems!

What is the measure of arc XZ if angle Y is inscribed in the circle and measures 60°?

Solve a geometry problem involving a circle where angle Y, an inscribed angle, measures 60°. Learn how to calculate the measure of arc XZ using the Inscribed Angle Theorem. Suitable for students in Grades 8-10.

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