WASHINGTON—The Federal Trade Commission is investigating Facebook Inc. over the use of personal data by an analytics firm tied to President Donald Trump’s campaign, a person familiar with the matter said.

The FTC is probing whether Facebook violated terms of an earlier consent decree when data of up to 50 million of its users was transferred to Cambridge Analytica, this person said. Under the decree, approved in 2012, Facebook agreed to get user consent for collecting personal data and sharing it with others.

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