Answer
B. 39°
Explanation
To solve this, we will use the outside angle theorem: the measure of an angle formed by two secants from a point outside the circle is half the difference of the measures of the intercepted arcs.
We can infer form our pictures that the intercepted arcs are [tex]XZ=114[/tex] and [tex]TS=36[/tex], so let's use our theorem:
[tex]XYZ=\frac{114-36}{2}[/tex]
[tex]XYZ=\frac{78}{2}[/tex]
[tex]XYZ=39[/tex]
We can conclude that the measure of angle XYZ is 39°
