Question

relating central angles and arc measures
complete the statements about circle z.
a central angle, such as angle of circle z, is an angle whose vertex is and whose sides are radii of the circle.
angle is not a central angle of circle z.
the degree measure of an arc is the degree measure of the central angle that intercepts it.
the measure of tu is degrees

Explanation:

Step1: Recall central - angle definition

A central angle of a circle has its vertex at the center of the circle. In circle \(Z\), an example of a central angle is \(\angle WZX\) (or other angles with vertex \(Z\)).

Step2: Identify non - central angle

An angle like \(\angle WXY\) is not a central angle since its vertex \(X\) is not at the center \(Z\) of the circle.

Step3: Apply arc - central angle relationship

The degree measure of an arc is equal to the degree measure of the central angle that intercepts it. For arc \(\widehat{TU}\), if the central angle \(\angle TZU = 79^{\circ}\), then the measure of \(\widehat{TU}\) is \(79\) degrees.

Answer:

• A central angle, such as angle \(\angle WZX\) of circle \(Z\), is an angle whose vertex is \(Z\) and whose sides are radii of the circle.
• Angle \(\angle WXY\) is not a central angle of circle \(Z\).
• The degree measure of an arc is equal to the degree measure of the central angle that intercepts it.
• The measure of \(\widehat{TU}\) is \(79\) degrees.