As you adjust the circle and the secant lines, you will see the angle measures and the arc measures change.
When the lines intersect INSIDE the circle, the measure of the angles is equal to the Average of the Intercepted Arcs.
When the lines intersect OUTSIDE the circle, the measure of the angles is equal to Half the Difference of the Intercepted Arcs!

As you adjust the circle and the secant lines, you will see the angle measures and the arc measures change.
When the lines intersect INSIDE the circle, the measure of the angles is equal to the Average of the Intercepted Arcs.
When the lines intersect OUTSIDE the circle, the measure of the angles is equal to Half the Difference of the Intercepted Arcs!