Question

Please see attatchment for question. Please include all postulates/theorems used to solve it, if possible. Also include the letter (A,B,C, or D).

Answer 1

1. If two secants intersect to form the vertex of an angle outside a circle and the sides of the angle intercept arcs on the circle, then the measure of the angle is equal to one-half the difference of the measures of the arcs intercepted by the sides of the angle.  A prudent auxiliary line is a chord connecting points of intersection of the sides of the angle with the circle as shown at the right.  
2. Inscribed angle theorem.   The measure of an inscribed angle is equal to one-half the measure of its intercepted arc. 

According to 2. : measure of arc RT = 2 m (angle S) = 60
Apply 1. : m(angle U) = (arc RS - arc RT )/2 = (84 - 60)/2 = 12