Question

which expression gives the measure of ∠xyz? a. $\frac{1}{2}(110^{circ}+42^{circ})$ b. $110^{circ}+42^{circ}$ c. $110^{circ}-42^{circ}$ d. $\frac{1}{2}(110^{circ}-42^{circ})$

Explanation:

Step1: Recall angle - measure formula

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

Step2: Identify intercepted arcs

The larger intercepted arc is $110^{\circ}$ and the smaller intercepted arc is $42^{\circ}$.

Step3: Apply the formula

The measure of $\angle XYZ=\frac{1}{2}(110^{\circ}-42^{\circ})$.

Answer:

D. $\frac{1}{2}(110^{\circ}-42^{\circ})$