Answer:
B. \(12^{\circ}\)
Step-by-step explanation:
We have been given an image of a circle. We are asked to find the measure of angle U.
We have been given that measure of angle 's' is 30 degrees, so the measure of arc RT will be 2 times the measure of angle 's' as angle 's' is inscribed angle of arc RT.
\(\text{Measure of arc RT}=2\times 30^{\circ}\)
\(\text{Measure of arc RT}=60^{\circ}\)
We know that the measure of angle formed by intersecting secant and tangent outside a circle is half the difference of intercepted arcs.
Using Secant-tangent theorem, we can set an equation to find the measure of angle U as:
\(m\angle U=\frac{1}{2}\times (\text{Measure of arc RS}-\text{Measure of arc RT})\)
Substituting the given values in above equation we will get,
\(m\angle U=\frac{1}{2}\times(84^{\circ}-60^{\circ})\)
\(m\angle U=\frac{1}{2}\times(24^{\circ})\)
\(m\angle U=12^{\circ}\)
Therefore, the measure of angle U is 12 degrees and option B is the correct choice.
