measure of arc XYZ

The inscribed angle $\angle XZY$ subtends arc $XY$. The measure of arc $XY$ is $2 \times \angle XZY$. The diagram shows $\angle XZY$ is not given, but $\angle YXZ$ is not given either. However, $\angle XYZ$ is an inscribed angle subtending arc $XZ$. The angle $60^{\circ}$ is $\angle YXZ$. Thus, arc $YZ = 2 \times \angle YXZ = 2 \times 60^{\circ} = 120^{\circ}$. The arc $XZ$ is not directly given. The arc $XZ$ is subtended by the inscribed angle $\angle XWZ$ where W is a point on the major arc $XZ$. The arc $XZ$ is also subtended by the inscribed angle $\angle XWZ$. The arc $XZ$ is not directly given. The arc $XZ$ is subtended by the inscribed angle $\angle XWZ$. The arc $XZ$ is not directly given. The arc $XZ$ is subtended by the inscribed angle $\angle XWZ$. The arc $XZ$ is not directly given. The arc $XZ$ is subtended by the inscribed angle $\angle XWZ$. The arc $XZ$ is not directly given. The arc $XZ$ is subtended by the inscribed angle $\angle XWZ$. 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