“Open” is an adjective.
“Closed” is also an adjective.
They’re spelled differently, and the latter seems to be derived from the past participle of the verb “to close.” Participles are verbs acting as adjectives, and adjectives that began as participles would tend to look like “closed” or “annoying.”
The singing bird was adored by the crowd.
“Singing” - present participle acting as adj.
How do I know? Because I can do this:
The bird is singing. (Use it in the progressive tenses as a verb.)
The problem, once solved, began anew.
“Solved” - past participle acting as adj.
How do I know? Because I can do this:
This problem has been solved. (Use it in the perfect tenses as a verb.)
These two examples are not listed in dictionaries as adjectives, but you see that they can easily be used that way. That is the nature of participles.
Note that you could never say something was “close” if you mean it is “closed.” “Close” is an adjective meaning “near.”
“Disposed” is an adjective when it means “inclined.”
“Dispose” is just a verb.
Participles routinely act as adjectives, and some enter the dictionary as adjectives themselves once they’re ubiquitous in that form. They will still resemble the verbs they were taken from.
Other genuine adjectives derived from participles:
Missing
Moving
Educated
Drunk
Resolved
You could say the door is “opened,” but it sounds a bit absurd or unnecessary since we already have a proper adjective to convey that.
Sometimes we still use participles when we have proper adjectives that perform the desired function:
I found him impressing. - Participle as adj.
I found him impressive. - Adj.