Four years ago, the city sold the dilapidated Carolina Theatre on North Tryon Street for $1 to the Foundation for the Carolinas. On Monday night, local government sweetened the deal by kicking in $4.5 million to close the gap on a proposed $51.5 million makeover. Foundation CEO Michael Marsicano pointed to a total investment of $145.5 million at the theater site, almost all of it from private sources, as the basis for seeking public money. The $4.5 million approved by council on Monday will come from existing taxes on hotel rooms and rental cars. Reviving the theater — built in 1927 and closed in 1978 — will preserve local history while adding an arts and cultural venue that will host film festivals, lectures, speeches, musical performances and comedy shows, among other events, foundation executives told council members Monday.