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.<span> </span><span>2. Inscribed angle theorem. The measure of an inscribed angle is equal to one-half the measure of its intercepted arc. </span> 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
