Question

question 9 of 10 which expression gives the measure of ∠xyz? a. 110° - 42° b. 1/2(110° + 42°) c. 110° + 42° d. 1/2(110° - 42°)

Explanation:

Step1: Recall inscribed - angle theorem for angles formed by two chords

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 $42^{\circ}$.

Step3: Apply the formula

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

Answer:

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