Question

which circle with center u shows a central angle whose intercepted arc, $widehat{vz}$, measures 58°?

Explanation:

Step1: Recall central - angle definition

A central angle is an angle whose vertex is the center of a circle.

Step2: Analyze each option

In the first option, the angle is not a central angle as its vertex is not at the center \(U\). In the third option, the angle is an exterior - type angle and not a central angle. In the fourth option, the angle is an inscribed angle (vertex on the circle) and not a central angle. The second option shows an angle with vertex at the center \(U\) and the intercepted arc \(\overset{\frown}{ZV}\) with a measure of \(58^{\circ}\).

Answer:

The second circle (the one with the angle having vertex \(U\) and measure \(58^{\circ}\))