Angie Polaski wears scarves in the show "Will Trent" mostly as a part of her character's style and possibly to metaphorically represent her guarded and complex nature. Some fans speculate the scarves might be used to symbolize something deeper, such as hiding vulnerabilities or past trauma, although there is no official explanation beyond it being a fashion choice for the character. Additionally, her scarves may also serve a practical purpose related to the character's storyline, including physical injury or cover-up, but this is more interpretative from audience discussions rather than confirmed behind-the-scenes info.
In summary, the scarves Angie Polaski wears reflect a combination of style, character symbolism, and possibly subtle storytelling about her background or current state, but no explicit canonical reason is widely known or provided by creators or actors.