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Works in English too:

* I am Danish.

* I am a Danish.

Or

* I am dancer.

* I am a dancer.

“I am dancer” is acceptable if you’re a five year old. However “I’m Danish” is correct English

In "I'm Danish" it's an adjective. With "I'm a Danish" it's a noun, stating you are a pastry.

You can say “I’m Danish” or “I’m British”. If you want to use an article and convey the same meaning then it would be “I’m a Dane” or I’m a Brit”

> A Danish pastry (sometimes shortened to Danish)

But only in US English!