To determine which sentences correctly use parentheses, we need to assess whether the information within the parentheses is supplementary and does not disrupt the flow of the main sentence. Here are the steps to evaluate each option:

Step 1: Evaluate the first sentence

“We went to the state fair (held in the state capital) for the first time this year.”

The information within the parentheses (“held in the state capital”) provides additional context about the location of the state fair without disrupting the main sentence. This usage is correct.

Step 2: Evaluate the second sentence

“For my birthday, my parents got me tickets to Hamilton (my favorite musical).”

The parentheses here (“my favorite musical”) clarify why the tickets were a meaningful gift. This usage is correct as it adds relevant detail without altering the sentence structure.

Step 3: Evaluate the third sentence

“My sister has homework for three classes tonight (math, English, and biology).”

The parentheses (“math, English, and biology”) list the specific classes, which is a clear and appropriate use of parentheses to provide detail.

Step 4: Evaluate the fourth sentence

“The student body voted to select (the person) who would get the Best Teacher award.”

The parentheses here (“the person”) are unnecessary as they do not add meaningful information and disrupt the flow of the sentence. This usage is incorrect.

Step 5: Evaluate the fifth sentence

“(When he made the hot chocolate) my brother left out the most important ingredient.”

The parentheses in this sentence (“When he made the hot chocolate”) are incorrectly used as they separate the subject from the action, making the sentence awkward. This usage is incorrect.

Final Answer

The sentences that correctly use parentheses are:

“We went to the state fair (held in the state capital) for the first time this year.”

“For my birthday, my parents got me tickets to Hamilton (my favorite musical).”