1. The problem asks for the measure of angle $XYZ$ in the given figure. 2. The figure shows a circle with center $O$, points $X$ and $Z$ on the circle along a horizontal line through $O$, and point $Y$ on the circle above this line. 3. Triangle $XYZ$ is formed by connecting points $X$, $Y$, and $Z$. 4. The angle $XYZ$ is marked with a right angle symbol, indicating it is a right angle. 5. By the property of a circle, an angle inscribed in a semicircle is a right angle (Thales' theorem). 6. Since $X$ and $Z$ lie on a diameter (horizontal line through center $O$), angle $XYZ$ is $90^\circ$. **Final answer:** The measure of angle $XYZ$ is $90^\circ$.