Dieser Fehler ist ärgerlich.

Because Fehler is a masculine noun, and here it is in the nominative singular.

German this changes to match gender, number, and case:

• dieser = masculine nominative singular
• diese = feminine nominative singular, or plural nominative
• dieses = neuter nominative singular

So:

• dieser Fehler = this error / this mistake
• diese Sache = this thing
• dieses Problem = this problem

It is in the nominative case, because it is the subject of the sentence.

In Dieser Fehler ist ärgerlich, the structure is:

• Dieser Fehler = subject
• ist = verb
• ärgerlich = predicate adjective

A useful point: after sein (to be), German does not use an object here. The subject stays in the nominative.

In this sentence, it is singular.

That is because both dieser and ist are singular:

• dieser Fehler ist = this error is

The noun Fehler has the same form in singular and plural, so the surrounding words tell you which it is.

Compare:

• Dieser Fehler ist ärgerlich. = singular
• Diese Fehler sind ärgerlich. = plural

Because it comes after the verb sein and is being used as a predicate adjective.

Predicate adjectives in German do not take adjective endings:

• Der Fehler ist ärgerlich.
• Das Problem ist groß.
• Die Aufgabe ist schwer.

But if the adjective comes before a noun, then it does take an ending:

• ein ärgerlicher Fehler
• das große Problem
• eine schwere Aufgabe

So:

• Dieser Fehler ist ärgerlich. → no ending
• ein ärgerlicher Fehler → ending appears

Here it means something like annoying, irritating, frustrating, or sometimes a nuisance.

It often describes something that causes annoyance. The best English choice depends on context.

For an inanimate thing like Fehler, the sense is usually:

• annoying
• frustrating
• irritating

In some contexts, ärgerlich can also mean regrettable, especially when something unfortunate has happened.

Yes. With a person, ärgerlich can mean annoyed, upset, or angry, depending on context.

For example:

• Ich bin ärgerlich. = I am annoyed / upset.

That said, many learners will also see verärgert, which is often a very clear way to say annoyed or angered.

So the meaning of ärgerlich depends a lot on what it describes:

• ein Fehler ist ärgerlich = the error is annoying
• ich bin ärgerlich = I am annoyed / upset

Because German main clauses usually follow the verb-second rule.

In a normal statement, the finite verb comes in the second position:

• Dieser Fehler | ist | ärgerlich

That is the standard word order for a simple statement.

German does not always keep the subject first, but it does usually keep the finite verb in second position in main clauses.

Yes, but the original sentence is the most neutral and natural version.

For emphasis, you could move another element to the front:

• Ärgerlich ist dieser Fehler.

This is grammatical, but it sounds more marked or literary. It puts extra focus on ärgerlich.

For most everyday situations, Dieser Fehler ist ärgerlich is the safest and most natural order.

Because dieser already functions as the determiner.

In German, words like dieser, jeder, welcher, and possessives like mein often take the place of the article rather than appearing next to it.

So you say:

• dieser Fehler
• mein Fehler
• jeder Fehler

Not:

• der dieser Fehler
• der mein Fehler

So dieser is already doing the job that der would normally do.

A rough English-style approximation is AIR-guh-likh, but that is only approximate.

A few pronunciation points:

• ä sounds a bit like the e in bet, though exact pronunciation varies
• the g is a hard g
• the r depends on accent, but in standard German it is often produced in the throat or weakened
• the final -ich has the soft German ch sound, like in ich, not an English k

A rough full-sentence approximation would be:

• DEE-zuh FAY-luh ist AIR-guh-likh

But it is best to listen to native audio if you can.

Because in German, all nouns are capitalized.

So:

• Fehler is a noun, so it gets a capital letter
• ärgerlich is an adjective, so it stays lowercase

This is one of the most noticeable spelling rules in German:

• der Fehler
• das Problem
• die Sprache

All of those nouns are capitalized.

Yes. That would also be correct, but it means something slightly different.

• Der Fehler ist ärgerlich. = the error is annoying
• Dieser Fehler ist ärgerlich. = this error is annoying

Dieser points more specifically to a particular error, often one that has just been mentioned or is being contrasted with another one.

So dieser is a bit more specific and demonstrative than der.