Why do adjective endings change with definite vs. indefinite articles.

Question

In German the endings of adjectives depend on whether the preceding article is definite or indefinite. Why?

Answer 1

Between the male and neutral indefinite article there is ambiguity. Both are "ein" in the Nominativ case.

Ein Hund. (male)

Ein Auto. (neutral)

When an adjective is added, it gets the gender specific ending to help with the ambiguity.

Ein brauner Hund.

Ein braunes Auto.

But with definite articles there is no ambiguity, since the gender is always clear. So all adjectives will have the generic ending (trailing -e).

Der braune Hund.

Das braune Auto.