The eldest son of José Martínez Polo and Juana Miquélez, Ángel was baptized at the age of one day; his aunt and godmother, Magdalena Martínez, consecrated him to the Virgin Mary. To get work, the family moved to Argentina when Ángel was five years old, but they were forced to return to Spain two years later when things didn’t work out. The boy‘s mother died when Ángel was seven years old. His aunt, Magdalena, helped with the family and ensured that the boys received a proper religious education. He went to a Piarist school, and began to feel a call to religious life. When he was old enough, he entered the Redemptorist seminary in Espino, Spain; a few years later, his younger brother Juan attended the same seminary.
Ángel was considered an excellent student, serious about his vocation, and a little stubborn. He was professed in the Redemptorists on 18 September 1928. He continued his studies, and was ordained a priest on 20 September 1930.
Father Ángel wanted to become a missionary, but his superiors decided that his work ethic and intelligence meant he would serve better as professor of philosophy and literature at the seminary at Astorga, León, Spain. The combination of the heavy teaching load and his own continued studies led to a collapse in January 1934. He was assigned to El Espino, Burgos, Spain to rest and recover; he used his time to hear confessions and preach missions and retreats. On 11 May 1934 he was assigned to the Redemptorist community in Granada, Spain, and then assigned to work as secretary to the Community of Perpetual Help in Madrid, Spain on 6 October 1934. He organized the library there, preached retreats, and wrote articles for Revista del Perpetuo Socorro.
In July 1936, just as the Spanish Civil War broke out, Father Ángel was assigned to minister to young people in the community. On 20 July, the street fighting reached the Community, and the Redemptorist brothers were seized by militiamen, accused of being Fascists because they opposed Communism. The Communists considered this just as bad, beat the brothers severely, and then shot them. His memorial is kept on the day of his martyrdom, July 20.