Question

which expression gives the measure of $\angle abc$?
a. $110^\circ - 20^\circ$
b. $\frac{1}{2}(110^\circ - 20^\circ)$
c. $110^\circ + 20^\circ$
d. $\frac{1}{2}(110^\circ + 20^\circ)$

Explanation:

Step1: Recall external secant angle rule

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

Step2: Identify intercepted arcs

The intercepted arcs are $\overset{\frown}{AC} = 110^\circ$ and $\overset{\frown}{AE} = 20^\circ$.

Step3: Apply the formula

The formula for $\angle ABC$ is $\frac{1}{2}(\text{measure of larger arc} - \text{measure of smaller arc}) = \frac{1}{2}(110^\circ - 20^\circ)$

Answer:

B. $\frac{1}{2}(110^{\circ} - 20^{\circ})$