Question

what is the measure of ∠xyz shown in the diagram below? a. 36° b. 39° c. 75° d. 78°

Explanation:

Step1: Recall angle - secant formula

The measure of an angle formed by two secants is $\frac{1}{2}$(difference of the intercepted arcs).

Step2: Identify intercepted arcs

The larger intercepted arc is $114^{\circ}$ and the smaller intercepted arc is $36^{\circ}$.

Step3: Calculate the measure of $\angle XYZ$

$\angle XYZ=\frac{1}{2}(114 - 36)=\frac{1}{2}\times78 = 39^{\circ}$

Answer:

B. 39°