Этот ангел очень красивый.

Because ангел is a masculine singular noun, and the demonstrative этот has to agree with it.

• этот = this (masculine)
• эта = this (feminine)
• это = this (neuter)
• эти = these (plural)

So:

• этот ангел = this angel
• эта книга = this book
• это письмо = this letter

Even though English just uses this for everything, Russian changes the form.

In Russian, nouns have grammatical gender. Ангел is a masculine noun.

A common pattern is:

• nouns ending in a consonant are often masculine
• nouns ending in -а / -я are often feminine
• nouns ending in -о / -е are often neuter

Since ангел ends in a consonant, it follows the usual masculine pattern.

Also, because it refers to a male-looking or male-coded being in many contexts, masculine agreement feels natural here, but the main reason grammatically is that ангел is just a masculine noun.

Because adjectives in Russian must agree with the noun they describe.

Since ангел is masculine singular, the adjective also has to be masculine singular:

• masculine: красивый
• feminine: красивая
• neuter: красивое
• plural: красивые

So:

• красивый ангел = a beautiful angel
• красивая девушка = a beautiful girl
• красивое здание = a beautiful building

In your sentence, красивый matches ангел.

In the present tense, Russian usually does not use a verb meaning "is" in simple statements like this.

So:

• Этот ангел очень красивый. literally works like This angel very beautiful.

But in natural English, we translate it as:

• This angel is very beautiful.

This is completely normal in Russian. The present-tense to be is usually omitted.

Очень means very. It usually goes before the adjective or adverb it modifies.

So:

• очень красивый = very beautiful
• очень быстро = very quickly

In this sentence:

• Этот ангел очень красивый.
• очень strengthens красивый

Its position is normal and natural here.

Yes. Russian word order is more flexible than English word order, although some versions sound more neutral than others.

The most neutral version here is:

• Этот ангел очень красивый.

You could also hear:

• Очень красивый этот ангел.
• Этот красивый ангел. (but this means more like this beautiful angel rather than this angel is beautiful)
• Красивый этот ангел. (possible, but more marked or expressive)

So word order can change, but it often changes the emphasis, not the core meaning.

Because here красивый is being used as part of the predicate: it tells you something about the angel.

Compare:

• красивый ангел = a beautiful angel
  (adjective directly describing the noun)

• ангел красивый = the angel is beautiful
  (predicate use)

In your sentence:

• Этот ангел очень красивый.

the structure is basically:

• This angel
  • very beautiful

So красивый is not just attached to the noun inside one noun phrase; it is the main description of the whole sentence.

Yes, but it is a slightly different form.

Russian has:

• the full form adjective: красивый
• the short form adjective: красив

Both can mean beautiful in this kind of sentence, but they are used a bit differently.

• Этот ангел очень красивый. — very common, neutral, natural in conversation
• Этот ангел очень красив. — also correct, often a bit more literary, formal, or stylistically marked

For many learners, the full form красивый is the safer and more common choice at first.

A rough pronunciation guide:

• этот ≈ EH-tuht
• ангел ≈ AHN-gyel
• очень ≈ OH-chin'
• красивый ≈ kruh-SEE-vy

A few useful notes:

• In этот, the stress is on the first syllable: Этот
• In ангел, the stress is on ан: Ангел
• In очень, the stress is on the first syllable: Очень
• In красивый, the stress is on си: красивый

The unstressed vowels are reduced in real speech, so the words may sound less like their spelling than in English.

Because the л in ангел is softened by the following е.

In Russian, consonants are often either hard or soft, and vowels like е, ё, и, ю, я often make the previous consonant soft.

So in ангел:

• the г and especially the л are influenced by the е
• the л is not the same as a hard English l

This softness is an important feature of Russian pronunciation.

Yes. Ангел is in the nominative singular.

The nominative is used for the subject of the sentence, and here этот ангел is the subject:

• Этот ангел = this angel

Because the noun is nominative masculine singular, both этот and красивый also appear in matching masculine singular nominative forms.

Yes, absolutely.

• Ангел очень красивый. = The angel is very beautiful / An angel is very beautiful
• Этот ангел очень красивый. = This angel is very beautiful

Adding этот makes the noun more specific: you are pointing out this particular angel.

Without этот, the sentence is still correct, but it is less specifically anchored to one identified angel.