Her friend and executor, John Quilty, told The New York Times Engel, who was a Christian Scientist, did not consult doctors about her illnesses.
Famous for her helium-high voice and sunny demeanor, Engel played Ted Baxter's ditzy girlfriend Georgette on The Mary Tyler Moore Show, joining the show in 1972 and remaining with it until the 1977 series finale.
Much later in her career, Engel received three Emmy nominations for playing Pat McDougall on Everybody Loves Raymond.
She recalled that a possible Everybody Loves Raymond spinoff set to include her and Fred Willard never come to fruition, which she called a great disappointment.
Ilhan Omar of dismissing 9/11 attacks
White House press secretary Sarah Sanders speaks during a press briefing at the White House on March 11, 2019, in Washington . And they were doing it hypocritically, since this is the kind of thing each side tends to hate when the other side does it.
In 2006, she was in the original Broadway cast of "The Drowsy Chaperone". Her final TV role was a Season 2 episode of Netflix's One Day at a Time.
The musical, about older adults who school themselves in hip hop to perform in half-time shows, was staged in New Jersey a year ago.
Engel reunited with "Mary Tyler Moore's" Gavin MacLeod in 2018.
Television writer and producer Phil Rosenthal, who is best known as the creator, writer, and executive producer of the sitcom "Everybody Loves Raymond", shared condolences on Twitter, saying: "To our dear sweet friend, we'll love and miss you and your brilliant talent always".
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