I need to tell if these sentences are Nonessential or Essential adjective clauses.

1.May gave the key to her mother who opened the door.....I have nonessential and placed comma after mother.

2.A man who lived in this town sailed his little boat across the Atlantic....I have nonessential and put commas after man and town.
Thank you for your help.

You are correct for the first sentence. The "who" clause is nonessential because "her mother" is already a clearly identified person as the antecedent.

The second sentence, though, is the opposite. Without the "who" clause, it could be referring to any man. The "who" clause is NEEDED (essential) to clearly identify the person who is the antecedent. Therefore, no commas are needed.

Thank you very much. I'm on my way to school. Have a good day.

You're very welcome!

To determine if the adjective clauses in the given sentences are nonessential or essential, you need to identify if they provide essential or nonessential information to the sentence.

1. "May gave the key to her mother who opened the door."
To determine if the adjective clause is nonessential, consider if the information in the clause is necessary to identify which mother is being referred to. If removing the adjective clause does not change the meaning or clarity of the sentence, then it is nonessential.
In this case, if you remove the clause "who opened the door," the sentence still makes sense: "May gave the key to her mother." Therefore, the clause is nonessential. To indicate this, you should place commas before and after the nonessential clause:
"May gave the key to her mother, who opened the door."

2. "A man who lived in this town sailed his little boat across the Atlantic."
Again, consider whether the adjective clause provides essential information for understanding the sentence. If removing the clause significantly alters the meaning or clarity, then it is essential.
If you remove the clause "who lived in this town," the sentence becomes ambiguous: "A man sailed his little boat across the Atlantic." Without the adjective clause, the reader might wonder which man is being referred to. Therefore, the clause is essential and should not be punctuated with commas:
"A man who lived in this town sailed his little boat across the Atlantic."

In summary:
1. May gave the key to her mother, who opened the door. (Nonessential)
2. A man who lived in this town sailed his little boat across the Atlantic. (Essential)