Angel was home schooled as a child. Her father fled religious persecution and settled in New York, where she joined him in 1914; a sister and brother who refused to leave Russia later perished during the Holocaust.
Her father was artistically talented, sketching in his spare time, and he encouraged Rifka to do the same, but she was 25 before she took up art seriously. She later said "her desire to create art was born out of the turmoil of her early life and her need to find peace of mind."
While a student of Boardman Robinson at the Art Students League of New York, she was especially inspired by fellow students John Sloan, Ernest Fiene, Emil Ganso, Ben Shahn, Max Kuhn and Alfred Maurer. She posed for Kuhn in the 1920s, and Ganso recommended her to Erhard Weyhe who selected several of her gouaches for his Weyhe Gallery. But Robinson encouraged her to quit school and focus on her spontaneous style.
Her first husband, George Brodsky, encouraged her to try watercolor painting. She showed some of her works to Sloan, who used his influence to get her work into some exhibitions.
In 1927, Angel returned to Russia for two years to visit a sister. While studying there, she was influenced by the styles of Matisse and Cezanne. On the way home she spent time in Paris, visiting museums and sketching.
Angel was one of the first artists in the United States to use a true encaustic technique, mixing beeswax with pigment in muffin tins and fusing according to a formula developed by her husband.
She was part of the Easel Division of the Illinois Federal Art Project.