The correct phrase is actually "hung up one's hat" and not "hanged up one hat". The phonetic transcription for "hung" is /hʌŋ/ and for "hanged" is /heɪŋd/. The past tense of hang is typically "hung", although "hanged" is used when referring to the execution of a person by hanging. In the phrase, "hang up one's hat" means to settle down in a particular place or situation, akin to hanging up one's coat or hat at the end of a long day.
"Hanged up one's hat" is an idiomatic expression which refers to the act of settling down or establishing oneself in a particular place or situation. It conveys the idea of finding a home, a job, or a role in a community where an individual feels comfortable or content.
The phrase originates from the act of a traveler, pioneer, or immigrant hanging their hat on a hook upon arriving at a new location. This action symbolizes a personal declaration of one's intention to stay and make a place their own. Thus, "hanging up one's hat" has come to represent the act of deciding to stay in a specific environment or situation for an extended period and accepting it as one's home or profession.
The expression is often used figuratively to describe a person who has finally found their niche in life or achieved a sense of belonging. It signifies a point of resolution or stability in one's life journey, reflecting a sense of accomplishment and security in a chosen endeavor.
Overall, "hanged up one's hat" conveys the idea of finding a settled position, establishing oneself, and feeling a sense of belonging in a particular place or situation.