Julie charmed audiences as Maria, who captured the heart of their widowed dad Captain Georg Von Trapp, played by Christopher Plummer.
"It's a movie that so many generations connect to young and old," Angela said. "Can you think of another film that has had such an effect for so long?"
Angela, 72, also appeared in Lost in Space between 1965 and 1968 and had a cameo in Netflix's 2018 reimagined version of the show. But it is for the timeless The Sound of Music that she will always be remembered.
She says of the film's leading lady: "We didn't really know who Julie was when we met her. Nobody had seen Mary Poppins when we filmed but our director Robert Wise knew that she was a star in the making.
"I had read the book [Mary Poppins] so I knew the story but I didn't know it was going to be such a cute movie."
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Angela and her fellow Von Trapp children were delighted when Julie taught them the songs from the 1964 musical co-starring Dick Van Dyke.
"She taught us all the lyrics to all the songs A Spoonful of Sugar and Supercalifragilisticexpialidocious and she taught us to sing that backwards, which I can still say," she laughs.
"Julie was so sweet and very smart. She endeared herself to us. Between takes she sang, and we would dance. We adored her. It really shows in the film itself, which is one of the reasons I think it was so successful.
"She is a very strong woman. I think Mary Poppins and The Sound of Music were both kind of sweetzy roles.
"She's a lot funnier than that. She often says she has the mouth of a sailor."
Set in late 30s Austria, just before World War II, the film broke box office records, becoming the then highest-grossing film of all time and winning five Academy Awards.
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By the time it came out, Angela was already on the path to child stardom.
She was born in Altrincham, Cheshire, and moved to America as a baby with her parents and elder sister.
"It was after the war and there were no homes," she says of her family's decision to emigrate.
"My mom had always dreamed of coming to America, so we all got on a boat and went to America to fulfil the American dream, which they never thought would include showbusiness in a million years. We were in Canada for a year until we were able to enter the US, because you had to be sponsored. The woman who was living down the hall from us had a child that did commercials and she said to my mum, 'oh your kids are cute you should go and see this agent'. It was just meant to be."
Angela was a successful child actor by the time, at 12 years old, she became Brigitta and started filming in Salzburg, Austria. "It was supposed to be for five weeks but, because of the rain, it was three months," she recalls, speaking from her home in Dallas, Texas.
Meticulous rehearsals meant everyone was word perfect when they arrived in Austria.
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"We knew the roles, songs and the script inside out," says Angela, who only recalls one mishap. We knew where we had to stand on the faux steps for Do-Re-Mi [filmed at Mirabell Gardens, in Salzburg]. That had taken a lot of practice.
"But I remember Heather [Heather Menzies, who played Louisa] was annoyed that she had made a mistake.
"She would say, 'why was that take chosen for the final edit?'. She ends up on the wrong step and she looks very sheepish at the end and kind of steps back. But I think that take was chosen because director Robert Wise wanted it not to be perfect. He wanted the kids to be real. He didn't want little robots.
"In the stage versions, all the kids were blonde, blue-eyed perfect. We were all very different.
The five surviving Von Trapp child actors (Charmian Carr and Heather Menzies had both died) were reunited in 2022 to honour Julie, now 89, when she received the American Film Institute's Life Achievement Award.
Meanwhile, Angela, who has been a photographer for 30 years, still has a die-hard fan base, despite barely acting for 40 years. "People can be really over the top when they find out I'm Brigitta," she chuckles. "They even say I look the same but I don't believe them."
Angela auditioned for two roles Brigitta and Louisa.
"I got Brigitta instead of Louisa but I was more like Brigitta, so I was glad to be playing her," she says of her character, who was very observant.
"That is me! But I was never as outspoken as Brigitta." Heather and Angela became great friends.
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"Heather and I were very close. We became fast friends as soon as we met," she says. "We were wild about The Beatles and we were so close in age."
Heather, who went on to have a successful film and TV career and married actor Robert Urich, also modelled for Playboy magazine, appearing in a controversial nude photosho...