Which of the following correctly matches the unit of seconds in angular measurement?

The correct match for seconds in angular measurement is that one second is equal to 1/60th of a minute. This relationship is fundamental in understanding how angles are measured in degrees, minutes, and seconds (DMS). In this system, each degree is divided into 60 minutes, and each minute is further divided into 60 seconds. Therefore, because a second is defined as a division of a minute, the option stating that one second is 1/60th of a minute accurately reflects this hierarchical structure of angular measurement.

The invalid options include the one that suggests a second is 1/60th of a degree, which does not correctly represent the relationship in angular measurements. Similarly, choices that reference overall measurements like 360 degrees or 30 minutes do not pertain specifically to the unit of seconds, as they refer to larger or different units within the angular measurement system.