Question

A circle is shown. 2 secants intersect outside of the circle to form angle 1. The measure of the first arc formed is b degrees, and the angle of the second arc is a degrees. Arc c degrees is outside of the secants.
Which formula would be used to find the measure of angle 1?

One-half(a° + b°).
One-half(a° – c°).
One-half(b° + c°).
One-half(a° – b°).

Answer 1

One-half(a° – b°).

Reason: For two secants intersecting outside a circle, the angle equals half the difference of the measures of the intercepted arcs (outer arc minus inner arc). Here a and b are the intercepted arcs, so angle1 = 1/2(a − b).