Question

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 (widehat{tu}) is degrees.

Explanation:

Step1: Identify central angles

A central angle has its vertex at the center of the circle. In circle \(Z\), \(\angle WZX\) (or \(\angle XZW\)) is a central angle as its vertex is \(Z\) (the center of the circle) and its sides \(ZW\) and \(ZX\) are radii.

Step2: Check non - central angles

\(\angle WSX\) is not a central angle because its vertex \(S\) is not the center of the circle \(Z\).

Step3: Recall arc - central angle relationship

By the definition of arc measure, the degree measure of an arc is equal to the degree measure of the central angle that intercepts it.

Step4: Find the measure of arc \(TU\)

The measure of arc \(TU\) is equal to the measure of the central angle \(\angle TZU\). Given \(\angle TZU = 79^{\circ}\), so the measure of arc \(TU\) is \(79^{\circ}\).

Answer:

A central angle, such as angle \(WZX\) (or \(XZW\)) of circle \(Z\), is an angle whose vertex is \(Z\) (the center of the circle) and whose sides are radii of the circle. Angle \(WSX\) 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 \(\overset{\frown}{TU}\) is \(79\) degrees.