Answer: [tex]ZYX=60\°[/tex]
Step-by-step explanation:
It is important to remember that, by definition:
[tex]Tangent\ chord\ Angle=\frac{1}{2}Intercepted\ Arc[/tex]
In this case you know that for the circle shown in the figure, the arc XY measures 120 degrees, therefore you can find the measure of the angle ZYX. Then you get that the measure of the this angle is the following:
[tex]ZYX=\frac{1}{2}XY\\\\ZYX=\frac{1}{2}(120\°)\\\\ZYX=60\°[/tex]
