The measure of an angle formed by two secants intersecting outside the circle equals
½ the sum of the intercepted arcs
½ the difference of the intercepted arcs
½ the measure of the intercepted arc
(b) as your text surely stated.
The measure of an angle formed by two secants intersecting outside the circle equals half the difference of the intercepted arcs.
To understand this concept, let's consider a circle with two secants intersecting outside the circle. When these secants intersect, two arcs are formed inside the circle - one on each side of the angle.
Now, imagine drawing radii from the center of the circle to the points of intersection of the secants. These radii will divide the circle into two sectors.
The measure of each sector is equal to the measure of the intercepted arc plus the measure of the angle formed by the secants. Thus,
Measure of Sector 1 = Measure of Intercepted Arc 1 + Measure of Angle
Measure of Sector 2 = Measure of Intercepted Arc 2 + Measure of Angle
Since the two sectors together make up the entire circle, their measures add up to 360 degrees:
Measure of Sector 1 + Measure of Sector 2 = 360 degrees
Substituting the above expressions, we get:
Measure of Intercepted Arc 1 + Measure of Angle + Measure of Intercepted Arc 2 + Measure of Angle = 360 degrees
Simplifying:
Measure of Angle = (360 degrees - Measure of Intercepted Arc 1 - Measure of Intercepted Arc 2) / 2
Thus, the measure of an angle formed by two secants intersecting outside the circle equals half the difference of the intercepted arcs.