Given the following figure with one tangent and one secant drawn to the circle, what is the measure of ?

Given the following figure with one tangent and one secant drawn to the circle, what is the measure of

?

A . 50
B . 85
C . 60
D . 110
E . 25

Answer: E

Explanation:

The measure of an angle in the exterior of a circle formed by a tangent and a secant is equal to half the difference of the intercepted arcs. The two intercepted arcs are

which is 60°, and

which is

110°. Find half of the difference of the two arcs: 1/2 × (110 C 60) = 1/ 2 × 50 = 25º.