Der Ärmel meiner Jacke ist nass geworden, aber der Kragen ist noch trocken.

Yes. Ärmel and Kragen are both masculine nouns in German, so in the nominative singular they take der:

• der Ärmel = the sleeve
• der Kragen = the collar

In this sentence, both are the subjects of their clauses:

• Der Ärmel meiner Jacke ist nass geworden
• der Kragen ist noch trocken

That is why both use der.

Because meiner Jacke is in the genitive case, which shows possession.

• der Ärmel meiner Jacke = the sleeve of my jacket / my jacket’s sleeve

The noun Jacke is feminine, and the genitive singular form with mein- is:

• meiner Jacke

So:

• meine Jacke = my jacket (nominative or accusative)
• meiner Jacke = of my jacket (genitive)

It is a very natural written and standard way, yes. German often uses the genitive for this kind of relationship:

• der Ärmel meiner Jacke
• die Farbe des Autos
• der Name meiner Schwester

In everyday spoken German, people also sometimes prefer von phrases:

• der Ärmel von meiner Jacke

But in standard German, especially in writing, der Ärmel meiner Jacke is usually preferred.

Because the sentence is describing a change of state.

• ist nass = is wet
• ist nass geworden = has become wet / got wet

So werden here means to become. The speaker is not just describing the sleeve’s condition; they are saying that it changed from dry to wet.

That is an important difference:

• Der Ärmel ist nass. = The sleeve is wet.
• Der Ärmel ist nass geworden. = The sleeve got wet.

Because werden forms its perfect tense with sein, not haben.

So:

• werden → ist geworden

This is common with verbs that show movement or a change of state.

Examples:

• Es ist kalt geworden. = It has gotten cold.
• Er ist müde geworden. = He has become tired.
• Der Ärmel ist nass geworden. = The sleeve got wet.

Geworden is the past participle of werden in this construction.

The verb is:

• werden = to become

Its participle is used in the perfect tense:

• ist geworden = has become / got

So in ist nass geworden, the full verbal idea is has become wet.

A useful thing to notice: the adjective stays separate.

• nass geworden = become wet
• not a single word meaning wet

Because nass is part of the predicate, and geworden is the participle of the verb werden.

German often builds this kind of structure as:

• sein + adjective + geworden

Examples:

• Er ist krank geworden. = He became ill.
• Das Wetter ist besser geworden. = The weather got better.
• Der Ärmel ist nass geworden. = The sleeve got wet.

So nass describes the new state, and geworden expresses the change into that state.

Because here nass and trocken are predicate adjectives, not adjectives placed before a noun.

Compare:

• der nasse Ärmel = the wet sleeve
  
  • adjective before the noun, so it takes an ending
• der Ärmel ist nass = the sleeve is wet
  
  • adjective after sein, so it does not take an ending

The same with trocken:

• der trockene Kragen = the dry collar
• der Kragen ist trocken = the collar is dry

Here noch means still.

So:

• der Kragen ist noch trocken = the collar is still dry

It suggests contrast with the sleeve:

• the sleeve has gotten wet,
• but the collar has not; it remains dry so far.

This is a very common use of noch.

Because it connects two main clauses:

• Der Ärmel meiner Jacke ist nass geworden
• aber der Kragen ist noch trocken

Aber means but. German word order after aber stays normal for a main clause. That means the subject comes next:

• aber der Kragen ist noch trocken

This is different from some other linking words that send the verb to the end. Aber does not do that.

Yes, you could. Both are possible, but they are a bit different in style and feel.

• Der Ärmel wurde nass. = The sleeve got wet.
• Der Ärmel ist nass geworden. = The sleeve has gotten wet / got wet.

In everyday spoken German, ist nass geworden is often very natural.
Wurde nass is also correct, but it may sound a bit more narrative or literary depending on context.

Learners should know both, but ist nass geworden is extremely common.

Here it is singular:

• der Ärmel = the sleeve

The word can look unusual because some German nouns do not change much in the singular. The plural is:

• die Ärmel = the sleeves

So:

• der Ärmel meiner Jacke = the sleeve of my jacket
• die Ärmel meiner Jacke = the sleeves of my jacket

Because it is understood from context.

The first clause says:

• Der Ärmel meiner Jacke = the sleeve of my jacket

Then the second clause says:

• aber der Kragen ist noch trocken = but the collar is still dry

Naturally, the listener understands this means the collar of the same jacket. German, like English, often leaves out repeated information when it is obvious.

A fuller version would be possible:

• ..., aber der Kragen meiner Jacke ist noch trocken.

But that sounds more repetitive unless you want extra emphasis.

The structure is:

• Der Ärmel meiner Jacke = subject
• ist = finite verb in second position
• nass geworden = rest of the predicate

So the pattern is:

• Subject + finite verb + complement/participle

This follows the standard German verb-second rule for main clauses.

Breaking it down:

• Der Ärmel meiner Jacke
• ist
• nass geworden

Even though nass geworden translates naturally as got wet, German separates the finite verb part (ist) from the participle (geworden).

They are completely different words:

• der Arm = arm, the body part
• der Ärmel = sleeve, the part of a piece of clothing

So:

• mein Arm = my arm
• der Ärmel meiner Jacke = the sleeve of my jacket

English speakers sometimes mix these up because a sleeve goes on an arm, but German keeps them clearly separate.