Dec 29, 2014 - I seem to recall that die Platte is more platter-like, larger, used for serving, and you eat off of der Teller. I could be wrong - it's been decades since I was in Germany.
In this sentence, "Teller" is in the accusative case, so being a masculine word, it requires "ein" to be declined to "einen."
Accusative appears any time there is a direct object. You shouldn't guide yourself by seeing the verb, but rather the sentence as a whole.
Could this be translated "The wife has a plate."? Which I suppose would mean "my wife" -- I'm still trying to figure out this usage. Germans (or maybe just Duolingo), seem to be big on using definite article for relatives.
"Die Frau" simply means "the woman". "Meine Frau" means "My woman" which more conversationally means "My Wife"