Angela is really pretty; she looks a lot like Violet Westing, who met a tragic end, and like her mother. That beauty's the first thing people notice about her, and it's usually all they give her credit for. Even Angela struggles to figure out who else she is, besides a pretty face, and has to work to create an identity for herself based on who she is, not just what she looks like. Other characters repeatedly refer to her as a "pretty thing," and many of them do treat her as a thing, rather than a person.
At the beginning of the book, when she's asked to define her position, she writes "none"; at the end, when her beauty has been altered by a scar and she's beginning to assert herself, she writes "person." It's probably significant that both she and other people start thinking of and treating herself as more like a person and less like a thing when her much-praised beauty has been damaged. When she's hurt on the outside, she finds strength on the inside.
Meanwhile, did you notice how Angela's linked to Chris several times in the book? People judge them based on how they look. When the heirs are originally put into teams, Theo worries that he's not his brother's partner, because he thinks he has to take care of Chris, and Grace worries that Dr. Deere isn't Angela's partner, because she thinks Angela needs someone to take care of her. Like Chris, people think of Angela as someone who needs to be cared for and as someone who's not able to do things based on her physical appearance. Even the narrator links them together, saying of her at one point that "her face [is] a mirror to the boy's [Chris's] suffering" (5.32).
Angela also has a problematic relationship with her mother. Let's face it, having Grace as a mother would probably screw up just about anyone. In a way, as the favorite child, Angela has it worse than Turtle does. Sure, Turtle is neglected, which is horrible, but Angela is hamstrung, bound, and limited by Grace. You know how women in China used to bind their feet, because small feet were a sign of beauty? They would constrict their feet's natural growth, bend them permanently out of shape, and end up hardly able to walk, all in the name of beauty. Well, Grace has treated Angela like one of these feet. Still with us? We'll explain. Grace has pushed Angela to depend entirely on her surface beauty, while deforming her character to keep her from being self-sufficient: Angela's dropped out of college, even though she had high grades and wanted to be a doctor; she's defined almost entirely by her relationship with Dr. Deere, although she doesn't even want to get married yet; she still lives at home with her controlling mother; and she doesn't know how to drive. She's dependent on her parents, and other people, for everything.
Because everyone is used to thinking of Angela as simply a pretty thing, incapable of doing anything on her own, it's a huge shock to find out that she's the bomber. It's she who damages the coffee shop and restaurant, puts herself and Sydelle in the hospital, and leads Turtle to take blame for something she didn't even do. Angela feels so trapped by her beauty and "thingness" that she willfully damages herself. By rejecting her beauty, and the kind of person that went with it, Angela slips back into normalcy. Once she's reclaimed her identity as a grown woman and aspiring doctor, she can re-consider her relationship with Dr. Deere and eventually become a mother herself.