Question

in the diagram of circle o, what is the measure of ∠abc? 30° 40° 50° 60°

Explanation:

Step1: Recall secant angle theorem

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The intercepted arcs are the major arc $\overset{\frown}{AC}$ ($210^\circ$) and the minor arc $\overset{\frown}{AC}$ ($150^\circ$).

Step3: Calculate the angle

$$\angle ABC = \frac{1}{2} \times (210^\circ - 150^\circ)$$
$$\angle ABC = \frac{1}{2} \times 60^\circ = 30^\circ$$

Answer:

30° (Option A)