The proposal now goes to the State Legislature, which votes Thursday on whether to exempt the proposal from the tax cap.
The measure would increase the county's sales tax to 8.75 percent, raising about $40 billion for expanded bus and rail lines and highway improvements.
Los Angeles County Supervisor Don Knabe revived the issue of whether to place the measure on the November general election consolidated ballot, and changed his "no" vote to "yes," giving the measure three votes on the five- member board.
City News Service contributed to this story.
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