Just a couple of rules are needed to solve this.
a) When secants cross inside a circle, the measure of the angle where they cross is the average of the measures of the intercepted arcs.
b) When secants meet outside the circle, the measure of the angle where they meet is half the difference of the measures of the intercepted arcs.
c) As a corollary to the first rule, if the secants meet on the circle, the angle where they meet is half that of the intercepted arc (because the other angle in the averge is zero).
