Question

question 1 of 10 which expression gives the measure of \\( \angle x y z \\) in the diagram below? a. \\( 154^{circ}-46^{circ} \\) b. \\( 154^{circ}+46^{circ} \\) c. \\( \frac{1}{2}\left(154^{circ}+46^{circ}\
ight) \\) d. \\( \frac{1}{2}\left(154^{circ}-46^{circ}\
ight) \\)

Explanation:

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

The measure of an angle formed by two secants intersecting outside a circle is given by \(\frac{1}{2}\) (difference of the measures of the intercepted arcs).

Step2: Identify the intercepted arcs

The intercepted arcs are \(154^{\circ}\) and \(46^{\circ}\).

Step3: Apply the formula

Using the formula \(\angle XYZ=\frac{1}{2}(154^{\circ}- 46^{\circ})\)

Answer:

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