Question

What is the measure of RST shown in the diagram below

Answer 1

Answer:

Answer is 64

Step-by-step explanation:

Answer 2

Answer:

A. $m\angle RST=64^o$

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).  

$m\angle RST=\frac{1}{2}(\text{Major arc- Minor arc})$

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,

$m\angle RST=\frac{1}{2}(153^o-25^o)$

$m\angle RST=\frac{1}{2}(128^o)$

$m\angle RST=64^o$

Therefore, measure of RST is 64 degrees and option A is the correct choice.