Question

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

Explanation:

Step1: Recall central - angle definition

A central angle has its vertex at the center of the circle.

Step2: Check 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 not a central angle as its vertex is not at the center \(U\). In the second option, the angle \(\angle ZUV\) has its vertex at the center \(U\) of the circle and the intercepted arc is \(\overset{\frown}{ZV}\) which measures \(58^{\circ}\).

Answer:

The second circle (the one with \(\angle ZUV = 58^{\circ}\) and vertex \(U\) at the center of the circle)