Definition from macmillandictionary.com
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She was wearing a brown fur hat.
She has to wear several different hats (=have various responsibilities) in her position.
Of course, when I say this, I’m wearing my teaching hat.
If you visit Surat, I'll eat my hat.
If I manage to do even one closure, I'll eat my hat.
If he comes back, I’ll eat my hat.
Let it never be said that Texas business leaders are all hat and no cattle.
I should look for other job vacancies. I can't hang my hat on this one.
Learning a new language is a skill you can hang your hat on