Question

question 2 of 10 which expression gives the measure of ∠xyz in the diagram below? a. 1/2(154° + 46°) b. 1/2(154° - 46°) c. 154° - 46° d. 154° + 46°

Explanation:

Step1: Recall the angle - subtended by arcs theorem

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

Step2: Identify the intercepted arcs

The larger intercepted arc is $154^{\circ}$ and the smaller intercepted arc is $46^{\circ}$.

Step3: Apply the formula

The measure of $\angle XYZ=\frac{1}{2}(154^{\circ}- 46^{\circ})$.

Answer:

B. $\frac{1}{2}(154^{\circ}-46^{\circ})$