Question

question 3 of 10
what is the measure of \\( \angle x y z \\) shown in the diagram below?

a. \\( 39^{circ} \\)
b. \\( 78^{circ} \\)
c. \\( 75^{circ} \\)
d. \\( 36^{circ} \\)

Explanation:

Step1: Recall the formula for the measure of an angle formed by two secants

The measure of an angle formed by two secants \( \angle XYZ=\frac{1}{2}(\text{measure of the intercepted arc } XZ-\text{measure of the intercepted arc } ST)\)

Step2: Calculate the measure of the intercepted arcs

The measure of arc \(XZ = 114^{\circ}\), the measure of arc \(ST=36^{\circ}\)

Step3: Substitute the values into the formula

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

Answer:

A. \(39^{\circ}\)