Respuesta :

Answer:

∠ZYX = 58°

Step-by-step explanation:

The measure of an inscribed angle or a tangent- chord angle is one half the measure of the intercepted arc.

arc XY is the intercepted arc, hence

∠ZYX = 0.5 × 116° = 58°

luisejr77

Answer: [tex]ZYX=58\°[/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}(116\°)\\\\ZYX=58\°[/tex]

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