There are several synonyms for the phrase "dangle a line" which is used in the context of fishing. One of the most commonly used synonyms is "cast a line." This term is used to refer to the motion of throwing a fishing line into the water. Other synonyms include "lure a line," "string a line," and "angle a line." These terms refer to the same action of fishing and can be used interchangeably based on personal preference. Regardless of the term used, the goal is always the same: to catch fish.