Ms. Roberts earned three Emmy Awards, was inducted into the Broadcasting & Cable Hall of Fame in 2000 and was named a “living legend” by the Library of Congress in 2008. The consummate Washington insider, she had covered Capitol Hill since the Carter administration and was eulogized after her death by former presidents George W. Bush and Barack Obama, who called her “a constant over 40 years of a shifting media landscape and changing world.”

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Her seasoned understanding of Washington politics was informed by an upbringing in Congress itself, where she bounced on the knee of House Speaker Sam Rayburn (D-Tex.), whom she called “Mr. Sam,” and was paraded through the halls by her father, Rep. Thomas Hale Boggs Sr. (D-La.). Hitting the campaign trail with a young Cokie in tow, he rose to become House majority leader before dying in a 1972 plane crash. His seat was filled by Ms. Roberts’s mother, Lindy Boggs, who launched her own nine-term congressional career.

Ms. Roberts inherited much of her parents’ unflappability and charisma, entering journalism in an era when the profession was dominated by men, especially in the political ranks. Her husband, Steven V. Roberts, was a New York Times correspondent in Greece, where Ms. Roberts began filing radio dispatches for CBS News as she watched the country’s military junta collapse in 1974.

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She later worked at NPR and PBS before joining ABC News in 1988, where she served as a political correspondent for “World News Tonight,” filled in for Ted Koppel on “Nightline” and appeared as a panelist on David Brinkley’s Sunday political program “This Week.” She anchored the show with Sam Donaldson from 1996 to 2002, when she was diagnosed with breast cancer.

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“Men come up to men on the street and say, ‘We like your common sense,’ ” she once said, recalling her early “This Week” years. “But women say, ‘We love the way you don’t let them interrupt you, and that you hand it right back to them.’ I get the feeling that the country is full of women who’ve never gotten a word in edgewise when men talk about politics.”

As her influence grew at ABC — and at NPR, where she continued working as a political commentator until her death — Ms. Roberts sought to fill the journalistic ranks with women. “Duck and file,” she advised aspiring female reporters: “Just do your work and get it on the air.”

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Ms. Roberts was the author of best-selling books, including several that focused on powerful women in American history, and wrote a syndicated political column with her husband, notably urging “the rational wing” of the Republican Party to stop the 2016 presidential nomination of Donald Trump.

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At times, she said, she yearned to step into politics like her parents and two siblings: Thomas H. Boggs Jr., a high-profile lobbyist and power broker, and Barbara Boggs Sigmund, who served as mayor of Princeton, N.J., before dying of cancer in 1990.

“I’m the only person in my original nuclear family who didn’t run for Congress. . . . I have always felt semi-guilty about it,” she told The Washington Post earlier this year. “But I’ve sort of assuaged my guilt by writing about it and feeling like I’m educating people about the government and how to be good voters and good citizens.”

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Ms. Roberts’s political connections led some media critics to question whether she was able to report dispassionately on friends and, in some cases, financial backers. Speeches that she and her husband delivered to corporations and special interest groups reportedly earned the couple as much as $45,000 in fees, and fueled criticism that Ms. Roberts — like other marquee names in Washington journalism — was merely echoing narratives of the political establishment.

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“Roberts doesn’t just voice the conventional wisdom; she is the conventional wisdom,” Slate media critic Jack Shafer wrote in 2009. Her four-minute NPR commentary segments, he added, “do little but speed-graze the headlines and add a few grace notes.”

For millions of viewers and listeners, however, Ms. Roberts was an indispensable guide to official Washington, able to explain knockout legislative fights and White House intrigue in snappy segments on David Letterman or Jay Leno’s late-night talk shows. She said she avoided stories in which there might be a conflict of interest, and saw little conflict in working for two media organizations at once, even if they were competitors.

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“I think it’s a woman’s talent,” she told The Post in 1993. “Being able to do two things at once.”

Mary Martha Corinne Morrison Claiborne Boggs was born in New Orleans on Dec. 27, 1943, and said her brother nicknamed her Cokie because he couldn’t pronounce Corinne.

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Her father, known as Hale, served in Congress for nearly three decades until his plane disappeared in Alaska en route to a campaign stop on behalf of a fellow Democrat. Ms. Roberts and her family were briefed daily on a search mission that never found the body, leaving her with a nagging sense of uncertainty.

“I know my father is not alive. . . . But still, I catch myself hesitating before changing the kitchen wallpaper, fearing that he will come home and think strangers are in the house,” she wrote in a 1991 New York Times op-ed. Her mother, the former Lindy Claiborne, took Hale Boggs’s seat in a special election and was later appointed by President Bill Clinton as U.S. ambassador to the Vatican.

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Ms. Roberts graduated from Stone Ridge School of the Sacred Heart, a Catholic girls’ school in Bethesda, Md., and received a bachelor’s degree in political science from Wellesley College in 1964. Her early journalism jobs included hosting a public affairs program at Washington television station WRC-TV and producing stints in New York and Los Angeles.

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She covered Capitol Hill for NPR beginning in 1978, when the media organization was still an upstart and, by some accounts, could only afford to hire inexperienced staffers, network castaways and women (who were paid less than men). Within NPR’s newsroom, Ms. Roberts and female broadcasters including Susan Stamberg, Nina Totenberg and Linda Wertheimer became known as the organization’s “founding mothers.”

“We had people tell us all along the way that we weren’t qualified to deliver the news, that we weren’t authoritative enough,” she told the Los Angeles Times in 1992. “We would have meetings with men in high positions and find their hands on our knees. We would have invitations from those people to hotel rooms. All kinds of propositions. Insults they didn’t consider insults.”

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“Those assaults make a difference in terms of how you think about yourself,” she added. “Maybe they’re right, you begin to think. Maybe I’m not authoritative. Maybe I’m not smart enough. And then you say to yourself, God, I went to the same schools as those guys. I have the same education as they do. What’s the problem? Why am I asked how many words a minute I can type when the guy next to me can’t type at all?”

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Ms. Roberts served as a congressional correspondent for more than a decade at NPR, which eventually installed a special line into her home so that she could call in to “Morning Edition” early in the day, in pajamas if necessary. At least one such broadcast was reportedly interrupted by the howling of her basset hound.

She married Roberts in a 1966 ceremony attended by President Lyndon B. Johnson and his wife, Lady Bird. They lived in Bethesda for many years and chronicled their marriage in a 2000 book, “From This Day Forward,” which also explored the history of marriage in America.

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In addition to her husband, survivors include two children, Lee Roberts of Raleigh, N.C., and Rebecca Roberts of Washington; and six grandchildren. Her mother died in 2013, her brother in 2014.

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Ms. Roberts remained a presence in the Capitol well after her cancer diagnosis, traipsing down halls that she had shuffled through as a child and run through as a reporter. “This is a friendly place,” she once told the Los Angeles Times. “It’s beautiful, it’s historic, and if it is true that I have a bias, it’s a bias in favor of the institution.”