Question

In the figure below, if arc XY measures 120 degrees, what is the measure of angle ZYX?

Answer 1

∠ZYX = 60°

Explanation:

The measure of an inscribed angle or tangent- chord angle is one half the measure of its intercepted arc, hence

∠ZYX = 0.5 × 120° = 60°

Answer 2

Answer:
`ZYX=60\°`

Explanation:

It is important to remember that, by definition:

`Tangent\ chord\ Angle=(1)/(2)Intercepted\ Arc`

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:

`ZYX=(1)/(2)XY\\\\ZYX=(1)/(2)(120\°)\\\\ZYX=60\°`