In the diagram below of circle C, the measure of arc QT = 140 degrees and the measure of arc P is 40 degrees. Find the measure of arc RS.
For an angle created by two secants: angle(P) = ½ · [ arc(QT) - arc(RS) ]
40 = ½ · [ 140 - arc(RS) ]
80 = 140 - arc(RS)
-60 = - arc(RS)
arc(RS) = 60
The angle equals one-half the difference of the two intercepted arcs.