 Rangel was born in Parral, Chihuahua, into a family formed by Rafael Rangel Romo, a mining engineer from Aguascalientes and co-proprietor of  (a flour mill) and Josefina Sostmann, he has a sister Josefina Rangel Sostman who is a painter.He undertook his secondary and preparatory studies in Parral at "Instituto Regional", a school managed by the Society of Jesus, and later moved to Monterrey to enroll at the Monterrey Institute of Technology.At Tech he imposed a national record in the 400 meters dash at the age of 22 and graduated with a bachelor's degree in Mechanical and Electrical Engineering in 1965.