Question

In the figure below, if arc XY measures 116 degrees, what is the measure of angle ZYX?

Answer 1

∠ZYX = 58°

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°

Answer 2

Answer:
`ZYX=58\°`

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)(116\°)\\\\ZYX=58\°`