Question

question 7 of 10
in the diagram below, \\( \overline { x y } \\) and \\( \overline { y z } \\) are tangent to \\( \odot o \\). which expression gives
the measure of \\( \angle x y z \\)?

\\( \bigcirc \\) a. \\( \frac { 1 } { 2 } ( 245 ^ { \circ } - 115 ^ { \circ } ) \\)
\\( \bigcirc \\) b. \\( \frac { 1 } { 2 } ( 245 ^ { \circ } + 115 ^ { \circ } ) \\)
\\( \bigcirc \\) c. \\( 245 ^ { \circ } + 115 ^ { \circ } \\)
\\( \bigcirc \\) d. \\( 245 ^ { \circ } - 115 ^ { \circ } \\)

Explanation:

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

The measure of an angle formed by two tangents drawn to a circle from an external point is half the difference of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The intercepted arcs are \(245^{\circ}\) and \(115^{\circ}\)

Step3: Apply the formula

The formula is \(\angle XYZ=\frac{1}{2}(\text{major arc}-\text{minor arc})\)
So \(\angle XYZ = \frac{1}{2}(245^{\circ}- 115^{\circ})\)

Answer:

A. \(\frac{1}{2}(245^{\circ}-115^{\circ})\)