Angeliki D. Cutchis, 52, director of the Tactical Air Forces Division in the Office of the Secretary of Defense, died of cancer Friday at Georgetown University Hospital.

Mrs. Cutchis joined the Defense Department in 1967. Before becoming director of the Tactical Air Forces Division, she had served as chief of the Combat Systems Division in the Office of the Assistant Chief of Staff for Force Development, Army, and as director of systems integration analysis with the Army's Concepts Analysis Agency.

Before 1967, she was a guided-missile-systems analyst at the Johns Hopkins University Applied Physics Laboratory for 16 years. In 1964, she became the first woman to be named a Parson's Fellow at Johns Hopkins University.

Mrs. Cutchis was born in New York City.She received a bachelor's degree in mathematics from Hunter College in 1949, and earned a master's degree in statistics from American University in 1963. She lived in Silver Spring.

A former president of the National Capital Chapter of the Hunter College Alumni Association, she had been admitted to the association's Hall of Fame.

She is survived by her husband, Pythagoras Cutchis, a son, Protagoras, and a daughter, Elektra, all of Silver Spring; her parents, Chrysostomos and Hero Demetriadis, of New York City, and a brother, Constantine, of Long Island, N.Y.