Is Angelou a strong woman in "Gather Together in My Name"? How can I support that with evidence from the text?

It can certainly be said that Angelou is a strong woman in this book. That is not to say that she is a paragon of virtue—on the contrary, this volume of her autobiography sets out the many and varied mistakes of her early life, because she feels that it is only by acknowledging the mistakes that she can grow and learn from them. But the choices Angelou makes mark her as a strong woman, a survivor, from the very beginning. 
In the first instance, purely in deciding to "take my beautiful son and go out into the world," Angelou risks the criticism and disapproval of her peers, as he is illegitimate. But Angelou is determined to prove herself "equal to my pride" and move out from under the feeling of guilt that she is a burden to her mother (prologue). 
Another indication of the writer's strength is when she approaches the Creole restaurant (Chapter 2) with "a lie as soft as butter" and pretends that the answer to the question "Can you cook Creole?" is "yes." It is a seventeen year old with a strong belief in herself who can spin such a lie and support it with the self-belief to go on and successfully prove herself in her determination to rise above a minimum-wage job. 
Perhaps Angelou's greatest triumph in this book, though, is her successful overhaul of her "little whorehouse." This section, from Chapter 12, gives countless examples of Angelou as a strong businesswoman, despite her lack of training. Angelou is unconventional, but hers is a story of survival against the odds.