Answer:
A. [tex]m\angle RST=64^o[/tex]
Step-by-step explanation:
We can see from our given diagram that angle RST is formed by intersection of two tangents of our circle.
We will use Tangent-Tangent Angle theorem, which states that if an angle is formed by two intersecting tangents, then the measure of the angle is one-half the difference of the measures of the intercepted arcs (the major arc - the minor arc).
[tex]m\angle RST=\frac{1}{2}(\text{Major arc- Minor arc})[/tex]
We can see that major arc is RT and minor arc is UV.
Upon substituting measures of our major arc and minor arc we will get,
[tex]m\angle RST=\frac{1}{2}(153^o-25^o)[/tex]
[tex]m\angle RST=\frac{1}{2}(128^o)[/tex]
[tex]m\angle RST=64^o[/tex]
Therefore, measure of RST is 64 degrees and option A is the correct choice.
