Glidelåsen på jakken min sitter fast, og det venstre ermet er vått.

Because glidelåsen is the definite singular form: the zipper.

• en glidelås = a zipper
• glidelåsen = the zipper

In Norwegian, the definite form is often made by adding an ending to the noun:

• en jakke → jakken
• en glidelås → glidelåsen

So Glidelåsen på jakken min means the zipper on my jacket.

Sitter fast is a very common expression meaning is stuck, is jammed, or won’t move.

Literally:

• sitter = sits
• fast = stuck / firm / fixed

But together, sitter fast is idiomatic. You should learn it as a set phrase.

Examples:

• Døra sitter fast. = The door is stuck.
• Lokket sitter fast. = The lid is stuck.

So in this sentence, it means the zipper is stuck, not that it is literally “sitting.”

Yes, literally på jakken min means on my jacket, and that works naturally in Norwegian for something that is physically attached to or part of the jacket.

So:

• Glidelåsen på jakken min = the zipper on my jacket

English often also says the zipper of my jacket, but Norwegian usually prefers på in cases like this.

Both are possible, but they are used differently.

• jakken min is the most common, neutral way to say my jacket
• min jakke is more emphatic, formal, or contrastive

So:

• jakken min = ordinary everyday my jacket
• min jakke = more like my jacket (as opposed to someone else’s)

This noun + possessive pattern is very common in Norwegian:

• boka mi = my book
• huset mitt = my house
• vennen min = my friend

Because erme is a neuter noun.

Its forms are:

• et erme = a sleeve
• ermet = the sleeve

For neuter singular nouns, the article used before an adjective in a definite phrase is det:

• det venstre ermet = the left sleeve

Compare:

• den røde jakken = the red jacket (jakke is common gender)
• det røde huset = the red house (hus is neuter)

So det tells you the noun is neuter.

In det venstre ermet, venstre is the adjective form used before a definite noun.

With a definite noun in Norwegian, adjectives usually take an -e ending:

• et vått erme = a wet sleeve
• det våte ermet = the wet sleeve

But some adjectives already end in -e or have forms that stay the same, and venstre is one of those forms used here:

• det venstre ermet = the left sleeve

So you can think of venstre as the normal attributive form in this phrase.

Because våt has to agree with ermet, which is neuter singular.

Adjective agreement:

• en våt jakke = a wet jacket (common gender)
• et vått erme = a wet sleeve (neuter)
• våte klær = wet clothes (plural / definite)

In the sentence:

• det venstre ermet er vått

the adjective vått is a predicate adjective after er, but it still agrees with the noun:

• ermet is neuter singular
• therefore våt becomes vått

Because the two noun phrases are built differently.

1. glidelåsen

This is a noun with the definite ending attached:

• glidelås → glidelåsen

No separate article is needed.

2. det venstre ermet

When a definite noun has an adjective before it, Norwegian usually uses double definiteness:

• a separate definite article: det
• and the noun also takes the definite ending: ermet

So:

• ermet = the sleeve
• det venstre ermet = the left sleeve

You can’t normally just say venstre ermet by itself in standard Bokmål when you mean the left sleeve.

The dictionary form is et erme.

Its common forms are:

• et erme = a sleeve
• ermet = the sleeve
• ermer = sleeves
• ermene = the sleeves

So ermet is just the definite singular form.

Because it connects two related facts smoothly:

• Glidelåsen på jakken min sitter fast
• det venstre ermet er vått

Using og works just like and in English. It is very natural when both things describe the same situation.

Also notice that the word order after og stays normal:

• det venstre ermet er vått

There is no inversion here, because og is just coordinating two main clauses.

Yes, but it would mean something slightly different.

• et venstre erme = a left sleeve
• det venstre ermet = the left sleeve

In your sentence, we are talking about a specific sleeve on a specific jacket, so Norwegian uses the definite phrase:

• det venstre ermet

If you were speaking more generally, you might use the indefinite form:

• Jakken har et venstre erme og et høyre erme.
• The jacket has a left sleeve and a right sleeve.

Yes, glidelås is the standard word for zipper in Norwegian.

Its forms are:

• en glidelås = a zipper
• glidelåsen = the zipper

A native English speaker may notice that the word is quite transparent once learned:

• gli relates to sliding/gliding
• lås means lock

But you do not need to analyze it every time; just learn glidelås as the normal everyday word.