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!