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SYDNEY (Reuters) - Australia’s center-right government will face a by-election in deposed prime minister Malcolm Turnbull’s seat on Oct. 20 and could lose its parliamentary majority if voter anger in opinion polls is carried through to the ballot box.

The by-election was announced on Wednesday following Turnbull’s resignation from parliament last month after he was ousted in a party-room revolt that ushered in Scott Morrison as the new prime minister.

It was the fifth change in prime minister since 2010, only one of which has been chosen at an election.

Turnbull’s resignation left Morrison presiding over a minority government, at least temporarily, although five independent lawmakers have guaranteed support to defeat no-confidence votes until the by-election.

Should the affluent electorate of Wentworth, which stretches from Bondi Beach to Sydney Harbour, be lost by the Liberal Party, Morrison would be forced to strike an agreement with the independents to continue in minority government.

A safe seat for the government under Turnbull, Wentworth is now expected to be a tight race as angry voters react to the political turmoil, a poll by The Australian newspaper showed.

While the Liberal Party candidate is still expected to win the biggest share of the vote in Wentworth, the ousting of Turnbull - a social liberal who was widely popular with voters - is expected see votes flow to opposition and minor candidates, who could win under Australia’s preferential voting system.

A Newspoll this week showed that national support for the ruling conservative coalition has plummeted following Turnbull’s ouster and would face a heavy defeat if national elections due by May 2019 were held now.

The political backlash was already felt when the Liberal Party, the senior partner in the Liberal-National coalition, saw a 29 percent swing against it at a New South Wales state by-election at the weekend where it lost what had been a safe seat to an independent candidate.