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 cent circle z.

the degree measure of an arc is the degree measure of
the central angle that intercepts it.

the measure of \\( \overgroup { t u } \\) is degrees.

Explanation:

• A central angle has its vertex at the center of the circle. In the given circle \(Z\), angle \(XSY\) (since \(S\) is not the center, but wait, no, actually, looking at the circle, the center is \(Z\). Wait, no, hold on. Wait, no, the first blank: A central angle is an angle whose vertex is the center of the circle. In the options, for the first dropdown, among \(WSX\), \(UZV\), \(XSY\), \(YSU\), the central angles (vertex at \(Z\)) is \(UZV\). Because a central angle's vertex is the center of the circle (\(Z\) in this case). For the second dropdown (not a central angle), among the options, if we assume the first correct central angle is \(UZV\), then \(WSX\) (vertex at \(S\), not \(Z\)) is not a central angle. The degree - measure of an arc is equal to the degree - measure of the central angle that intercepts it (by the central - angle - arc - measure theorem). For the measure of \(\overset{\frown}{TU}\), if we assume that the central angle for \(\overset{\frown}{TU}\) is \(79^{\circ}\) (from the diagram where the central angle at \(Z\) for \(T\) and \(U\) is \(79^{\circ}\)).

Answer:

1. \(UZV\), center (\(Z\))
2. \(WSX\)
3. equal to
4. \(79\)