Question

What is the measure of XYZ in the diagram below?

Answer 1

39°

Explanation:

Firstly, you can tell that YX and YZ are two secants of the circle. Therefore, you know that angle XYZ is an angle intercepted by secants.

An angle formed by two secants measures half the difference between the two arcs it intercepts.

This means that the measure of angle XYZ =
`(116 - 38)/(2)`

Let's calculate this value:

`(116 - 38)/(2)`

=
`(78)/(2)`

= 39

Therefore, the measures of angle XYZ is 39 degrees.

Hope this helps :)

Answer 2

39

Explanation:

angle formed by two secants=1/2(difference of intercepted arcs)

Y = 1/2 ( 116-38)

Y = 1/2 (78)

Y = 39