Meaning
To take the blame / To be the scapegoat
Example
Meu irmão quebrou o vaso e minha mãe pensou que foi eu, tive que pagar o pato!
My brother broke the vase and my mother thought it was me, I had to take the blame!
Origin
The Italian source 'pagare l'oca' (to pay the goose) already existed in the 16th century, tied to a folk tale in which a rural traveller tricks a peasant woman and leaves her husband to settle the bill for a goose he never bought. The tale spread to Portugal and then Brazil, where 'pato' (duck) replaced the goose.
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity