My answer is semantic, not grammatical. The issue is one of meaning, not of rules of syntax.
If you intend that there is one unique correct answer then "the right answer" is the correct meaning since the noun "answer" is fully determined by the adjective "right".
Similarly, there are usually many incorrect answers: so "That's a wrong answer" is correct and meaningful. You are wrong to say that this is not grammatical. Similarly, you can use "the perfect car" to imply that the car is fully determined by its perfection, but you can also use "a perfect car" to imply that there are others that are equally good.
So in all the examples you give, both "a" and "the" are grammatically possible. A native speaker would intuitively choose an article according to the meaning that they want to give.
Generally, adjectives that are incomparable will be more determining. If you can't be "righter" or "less right", then a noun will be fully determined by the adjective and so the article chosen will be "the".
This is an interesting construct and a great question.
Let's start by explaining it this way: Instead of using the proper name, use a generic word instead. Then the sentences will make a lot more sense:
Yesterday I met an angry woman at the cafe.
The astounded man could not say a word.
Those probably make sense, and articles do not seem odd or out-of-place.
When you substitute the person's name for the generic word, the sentence carries more meaning.
Yesterday I met an angry Kate at the cafe.
If I heard this, I would assume:
- You and I both know Kate – this wasn't some random stranger who was angry
- Kate is not usually angry – this isn't her usual mental state
Therefore, I'd probably answer with something like:
Oh? What was she angry about?
or:
What happened to Kate?
As for:
The astounded John could not say a word.
That pretty much says the same thing as
John was astounded and couldn't say a word
but it has a more poetic ring to it; you are ascribing a state of astonishment to John.
As for the other example in your comment:
Mike was accompanied by the beautiful Sara Hope.
This is different; in this case, I would interpret the definite article to mean that Sara Hope is a person with some fame or celebrity, and Mike was with the famous celebrity, not some unknown person who happened to have the same name.
At any rate, these constructs are grammatical and valid, but they are also a bit unusual. I would caution against overusing them in casual conversations.
Best Answer
Interchangeably? Perhaps not 100% "interchangeably." But either article could be used. The resulting implication is largely the same no matter which article is used, although how that conclusion is reached changes slightly depending on which article is used.
When it comes to rights, I may have several rights, such as:
Saying:
implies that I may have several rights (such as the four I just mentioned), but, right now, I'm talking about a different right: the right to be angry about some matter.
Saying:
means that I am justified in my anger, but it makes no implied acknowledgement about any other rights I may have. On the other hand, it does NOT imply that I don't have any other rights, so one could still use it.
When talking about rights, asking which article ought to be used can be tricky. We have legal rights, moral rights, ethical rights, parental rights, and personal rights; it largely depends on the context. I might say:
but what does that mean? And is it even true? Most people have the legal right to buy a cookie and eat it, but there could be religious convictions, personal reasons, parental restrictions, or dietary restrictions to prevent them from doing so: it might break a declared fast for Lent, violate a diet plan or lifestyle choice, break a family rule ("No dessert if you don't eat all your vegetables!"), harm the health of a diabetic, or cause an allergic reaction.
For your four examples, I have no problem with using either article, and I'm hard-pressed to explain a significant difference between the two, other than the trivial matter I've already gone over. I think you could even mix-and-match them:
(I can imagine a suspicious spouse saying that with no small amount of ire.)
For the last one, there are two ways that it could be interpreted:
could mean:
I'm trying to figure out whether or not one article tends to map better to one meaning, or if either article could be used to express both possible meanings. I'm inclined to believe it's the latter case, that is, either article could be used to discuss both an established legal right, and a gross grievance.
I realize I have rambled a bit here, but there are several contexts in which we can talk about rights, and I felt it was important to at least consider a few of them before reaching a conclusion. My bottom line answer is that, in some contexts, one article may sound a bit more natural than the other, but, for the most part, either one could be used, and they will pretty much mean the same thing.