Which protocol allows Cisco switches to dynamically determine their interface status without manual configuration?

The Dynamic Trunking Protocol (DTP) is the correct choice because it facilitates automatic negotiation of trunking on Cisco switches. When switches are connected, DTP allows them to dynamically determine whether an interface should operate as an access port or a trunk port. This helps streamline configurations by eliminating the need for manual settings, thus enhancing the ease of managing VLANs across multiple switches.

DTP continuously communicates between switches over a link to determine the best trunking method based on the capabilities of each switch involved. If both ends of the connection support trunking, DTP helps establish a trunk link automatically, simplifying network management.

In contrast, other protocols presented do not serve the same purpose. Link Aggregation Control Protocol (LACP) is designed for managing link aggregation, allowing multiple network interfaces to be bundled for increased bandwidth and redundancy but does not deal specifically with trunking. Spanning Tree Protocol (STP) is primarily used to prevent loops in network topologies by managing active paths but doesn't dynamically negotiate interface settings. EtherChannel Protocol refers to the broader concept of bundling multiple links but relies on protocols like LACP or PAgP to operate effectively.