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. 42 79 100 180

Explanation:

Step1: Define central angle

A central angle has its vertex at the center of the circle. In circle \(Z\), \(\angle WZX\) (for example) is a central - angle as its vertex is at \(Z\) (the center of the circle) and its sides are radii of the circle.

Step2: Identify non - central angle

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

Step3: Recall arc - central angle relationship

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

Step4: Find measure of arc \(\widehat{TU}\)

The central angle that intercepts arc \(\widehat{TU}\) is \(\angle TZU = 79^{\circ}\), so 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.