As per the outside angle theorem of a circle, the value of ∠XYZ is 69°
"The Outside Angles Theorem states that the measure of an angle formed by two secants, two tangents, or a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs."
Given, [tex]XZ =[/tex] 172°, [tex]ST =[/tex] 34°
Therefore, ∠XYZ
[tex]= \frac{(XZ - ST)}{2}\\[/tex]
[tex]= \frac{(172 - 34)}{2} degrees\\ = \frac{168}{2} degrees\\ = 69 degrees[/tex]
Learn more about the outside angle theorem of a circle here: https://brainly.com/question/10541581
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