Question

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

Explanation:

Step1: Recall the angle - measure theorem

The measure of an inscribed - angle formed by two chords is half the difference of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The larger intercepted arc is $110^{\circ}$ and the smaller intercepted arc is $20^{\circ}$.

Step3: Apply the formula

The measure of $\angle ABC=\frac{1}{2}(\text{major arc}-\text{minor arc})=\frac{1}{2}(110^{\circ}-20^{\circ})$.

Answer:

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