[2] Her paternal grandfather Owen Shanahan assisted in Irish republican John Boyle O'Reilly's escape from Western Australia.

[1] Tangney spent her early years in country Western Australia where her father was a locomotive driver and timber worker.

[1] When she was eight, her father found work in the port city of Fremantle where she attended St Joseph's Convent School.

She won a scholarship to attend St Joseph's College, selling raffle tickets to raise money for her school uniform.

[2] Tangney passed her leaving certificate at the age of 15 and began training as a schoolteacher, combining her teaching work with part-time study at the University of Western Australia.

She was eventually elected to the Western Australian Labor Women's Organisation Committee, and then to the party's state executive.

[1] She helped establish the University Labor Club, later serving as its president, and was also the founding president of the Fremantle Young People's Ideal Club in 1929, which organised activities for the children of the unemployed and was absorbed into the Western Australian Young Labor League.

[2] Tangney stood for the seat of Nedlands at the 1936 and 1939 Western Australian state elections, losing to her Nationalist opponent Norbert Keenan on both occasions.

[1] In 1954, Tangney was elected to the ALP's parliamentary executive with the support of the left faction, although some of her views were considered right-wing.

[1] In 1968, despite the ALP's objection to imperial honours,[2] Tangney became the first woman born in Western Australia to be appointed a Dame Commander of the Order of the British Empire (DBE).