Question

question 1 of 10
the measure of \\( \overleftrightarrow { xyz } \\) is \\( 296 ^ { \circ } \\). what is the measure of \\( \angle xzw \\), the tangent - chord angle?
a. \\( 116 ^ { \circ } \\)
b. \\( 206 ^ { \circ } \\)
c. \\( 148 ^ { \circ } \\)
d. \\( 296 ^ { \circ } \\)

Explanation:

Step1: Find the measure of the arc that is not \(\overarc{XYZ}\)

The total measure of a circle is \(360^{\circ}\). Let the measure of the arc that is not \(\overarc{XYZ}\) be \(m\). Then \(m = 360^{\circ}- 296^{\circ}=64^{\circ}\)

Step2: Use the tangent - chord angle formula

The measure of a tangent - chord angle is half the measure of the intercepted arc. The tangent - chord angle \(\angle XZW\) intercepts the arc whose measure is \(m = 64^{\circ}\). Let the measure of \(\angle XZW\) be \(x\). Then \(x=\frac{1}{2}(360^{\circ}-296^{\circ})\)

Answer:

A. \(116^{\circ}\)