muni jadongeuro dathyeoyo.

Because 문 is the subject here, not the direct object.

The verb is 닫히다, which means to close / to be closed. With this verb, the door is the thing that undergoes the action, so it takes the subject marker 이/가:

• 문이 닫혀요 = The door closes / is closed

  Compare that with 닫다, which is transitive and needs an object:

• 문을 닫아요 = Someone closes the door

So:

• 문이 닫혀요 → the door closes
• 문을 닫아요 → someone closes the door

자동으로 means automatically.

It comes from:

• 자동 = automatic operation / automation / automatic
• -으로 = a particle that can mean by, with, through, or can turn some nouns into adverb-like expressions

So 자동으로 literally has the sense of by automatic means, which is why it is naturally translated as automatically.

You will see this pattern a lot:

• 버스로 가요 = go by bus
• 한국어로 말해요 = speak in Korean
• 자동으로 열려요 = opens automatically

Because 닫혀요 comes from 닫히다, not 닫다.

• 닫다 = to close something
• 닫히다 = to close / to be closed

So the difference is:

• 문을 닫아요 = someone closes the door
• 문이 닫혀요 = the door closes / the door is closed

In this sentence, 닫혀요 is the natural choice because an automatic door is doing the closing by itself or through a mechanism, and the sentence focuses on the door, not on a person.

The dictionary form is 닫히다.

The polite present form is made like this:

• 닫히다 → stem 닫히-
• 닫히어요 → contracted to 닫혀요

This kind of contraction is very common in Korean.

So when you see 닫혀요, think:

• dictionary form: 닫히다
• meaning: closes / is closed

It is often taught as the passive counterpart of 닫다, and that is useful:

• 닫다 = to close
• 닫히다 = to be closed

But in real usage, 닫히다 often feels very natural as a plain intransitive verb too, especially in sentences like this one.

So 문이 자동으로 닫혀요 can be understood as:

• The door closes automatically
• or The door is closed automatically

In natural English, The door closes automatically is usually the best translation.

It is in the Korean present tense, but Korean present tense is broader than English present tense.

Depending on context, 문이 자동으로 닫혀요 can mean:

• The door closes automatically
  a general fact or feature
• The door is closing automatically
  something happening now
• The door gets closed automatically
  depending on context

If this is on a sign or someone is explaining how a door works, the most natural reading is usually The door closes automatically.

닫혀요 is in the standard polite -요 style.

This is the most common polite style in everyday Korean. It is appropriate in many normal situations.

Compare:

• 닫혀 = casual
• 닫혀요 = polite everyday style
• 닫힙니다 = formal polite style

So if this were written on a very formal notice, you might also see:

• 문이 자동으로 닫힙니다

But the meaning is basically the same.

No. It does not name an agent.

That is one reason 닫히다 is useful here. The sentence focuses on what happens to the door, not on who or what causes it.

In context, the cause could be:

• a machine
• a timer
• a sensor
• the door mechanism itself

But Korean does not need to state that here.

Yes, Korean word order is flexible because particles show each word’s role.

So these can all be possible depending on emphasis:

• 문이 자동으로 닫혀요
• 자동으로 문이 닫혀요

The first one is the most neutral and straightforward.

Even when the order changes, 이 still marks 문 as the subject, and 자동으로 still functions as automatically.

Yes, absolutely. It sounds like something you might hear or read when talking about an automatic door.

For example, it could be used:

• in conversation: 이 문은 자동으로 닫혀요
• as an explanation: 조심하세요. 문이 자동으로 닫혀요
• on a more formal sign: 문이 자동으로 닫힙니다

For signage, Korean often prefers a slightly more formal style, but the grammar is the same idea.