Ten kapelusz jest brzydki, ale bardzo wygodny.

Because kapelusz is a masculine singular noun, and ten is the form of this used with masculine singular nouns in the nominative.

A quick comparison:

• ten for masculine: ten kapelusz = this hat
• ta for feminine: ta książka = this book
• to for neuter: to okno = this window

So ten has to agree with kapelusz.

A very common clue in Polish is the ending of the noun.

Kapelusz ends in a consonant, and nouns ending in a consonant are often masculine. You can also see the masculine agreement in the sentence:

• ten kapelusz
• jest brzydki
• jest wygodny

All those words are in masculine singular forms, so they confirm the gender of kapelusz.

In Polish, adjectives must agree with the noun they describe in gender, number, and case.

Here, kapelusz is:

• masculine
• singular
• nominative

So the adjectives also appear in masculine singular nominative:

• brzydki = ugly
• wygodny = comfortable

If the noun changed, the adjective forms would change too:

• ta torba jest brzydka = this bag is ugly
• to krzesło jest brzydkie = this chair is ugly

They do match grammatically, even though the endings look different.

Both brzydki and wygodny are masculine singular nominative forms. The difference comes from the adjective stem and normal Polish spelling patterns, not from a difference in grammar.

For example:

• brzydki → feminine brzydka, neuter brzydkie
• wygodny → feminine wygodna, neuter wygodne

So they are both agreeing correctly with kapelusz.

In normal Polish, jest is usually needed in the present tense.

So:

• Ten kapelusz jest brzydki. = This hat is ugly.

Unlike some other Slavic languages, standard Polish normally does not omit the present-tense form of to be in regular sentences like this.

Learners should definitely include jest here.

Because Polish does not need a dummy subject like English often does.

In English, you might say It is ugly. In this Polish sentence, the subject is already stated:

• Ten kapelusz = this hat

So Polish simply says:

• Ten kapelusz jest brzydki

There is no need for an extra word meaning it.

Because ale means but, and in Polish it is standard to put a comma before ale when it joins two parts of a sentence.

So:

• Ten kapelusz jest brzydki, ale bardzo wygodny.

That comma is correct and natural.

Bardzo means very. It intensifies the adjective wygodny:

• bardzo wygodny = very comfortable

In Polish, bardzo usually goes before the adjective or adverb it modifies.

So:

• bardzo wygodny = very comfortable
• bardzo brzydki = very ugly

Here it only modifies wygodny, not brzydki.

The given word order is the most neutral and natural one:

• Ten kapelusz jest brzydki, ale bardzo wygodny.

Polish word order is more flexible than English, so other versions are possible for emphasis, but they may sound more marked.

For learners, this sentence is the best standard pattern:

• [this hat] + [is] + [ugly] + [but] + [very comfortable]

Because in this sentence the adjectives are part of the predicate after jest:

• The hat is ugly, but very comfortable

That is different from putting adjectives directly before the noun, as in:

• an ugly but very comfortable hat

In Polish, that second idea would be:

• ten brzydki, ale bardzo wygodny kapelusz

So both patterns exist, but they mean slightly different sentence structures:

• Ten kapelusz jest brzydki... = This hat is ugly...
• Ten brzydki kapelusz... = This ugly hat...

It is in the nominative singular.

That is because kapelusz is the subject of the sentence:

• Ten kapelusz = this hat

The adjectives brzydki and wygodny are also in nominative singular masculine because they describe the subject after jest.

A rough pronunciation guide is:

• Ten → like ten, but with a short clear e
• kapelusz → ka-pe-LOOSH
• jest → yest
• brzydki → approximately BZHIT-kee
• ale → A-le
• bardzo → BAR-dzo
• wygodny → approximately vy-GOD-nih

A useful general rule: Polish stress is usually on the second-to-last syllable:

• ka-pe-LUSZ
• BAR-dzo
• wy-GOD-ny

Not always. The Polish sentence matches English quite closely here, but it is still important to follow Polish grammar rules:

• use the correct form of this: ten
• make adjectives agree: brzydki, wygodny
• include jest
• put a comma before ale

So even when the meaning is easy, the grammar still has to be Polish, not just English words swapped one by one.