The measure of arc XYZ is 296 degrees. What is the measure of the tangent-chord ang...

The tangent-chord angle is half the measure of the intercepted arc. The arc intercepted by $\angle XZW$ is the minor arc $XZ$. The measure of the major arc $XYZ$ is $296^\circ$. Therefore, the measure of the minor arc $XZ$ is $360^\circ - 296^\circ = 64^\circ$. The measure of $\angle XZW$ is $\frac{1}{2} \times 64^\circ = 32^\circ$. However, the diagram shows that $\angle XZW$ intercepts the major arc $XZ$. The measure of the major arc $XZ$ is $296^\circ$. Therefore, the measure of $\angle XZW$ is $\frac{1}{2} \times 296^\circ = 148^\circ$.