Sigurvegarinn er ánægður.

Because Icelandic usually adds the definite article to the end of the noun instead of using a separate word like the.

• sigurvegari = winner
• sigurvegarinn = the winner

With many masculine nouns ending in -ari, the final -i drops before the definite ending -inn.

Er is the present-tense singular form of að vera, which means to be. Here it means is.

So:

• er = is
• eru = are (plural)

Because ánægður is a predicative adjective here: it comes after er and describes the subject.

Predicative adjectives in Icelandic normally agree with the subject in:

• gender
• number
• case

Since sigurvegarinn is masculine singular nominative, the adjective must be ánægður.

The form ánægði is a weak form usually used when the adjective comes directly before a definite noun, for example:

ánægði sigurvegarinn = the happy winner

But in Sigurvegarinn er ánægður, the correct form is ánægður.

Both are in the nominative.

• Sigurvegarinn is the subject, so nominative is expected.
• With að vera and similar linking verbs, the adjective describing the subject also stays in the nominative.

So this is not an object construction. It is a subject plus a description of that subject.

Not always exactly. It can mean happy, pleased, or satisfied, depending on context.

In this sentence, if someone has just won something, English could naturally translate it as either:

• The winner is happy
• The winner is pleased

So happy is a good translation, but pleased is often a very natural nuance.

Yes. This is a very normal basic sentence pattern:

subject + verb + complement

• Sigurvegarinn = subject
• er = verb
• ánægður = complement/adjective

Icelandic main clauses are usually verb-second, so if something else comes first, the verb still stays in second position. For example:

Í dag er sigurvegarinn ánægður = Today the winner is happy

You would change the noun, the verb, and the adjective so they all match the plural:

• sigurvegarinn → sigurvegararnir = the winners
• er → eru = are
• ánægður → ánægðir = happy in masculine plural

So the sentence becomes:

Sigurvegararnir eru ánægðir.