Select the most appropriate idiom from the options to replace the underlined segment in the given sentence.

After his business failed, he had to reduce spending and adjust to a frugal lifestyle.

The correct option is tighten his belt.

Step-by-step Explanation:

1. Analyze the underlined phrase:
The phrase "had to reduce spending" means to cut back on expenditures, live more frugally, or save money because of a financial constraint (in this case, his business failure).

2. Evaluate the idiom "tighten his belt":
To "tighten one's belt" is a common English idiom that means to spend less money than usual or to live more frugally, especially during a time of financial difficulty. This matches the meaning of the underlined segment perfectly.

3. Analyze the incorrect options:
• "hit the nail on the head": means to describe exactly what is causing a situation or problem, or to be precisely correct.
• "let the cat out of the bag": means to accidentally or prematurely reveal a secret.
• "kick the bucket": is an informal euphemism that means to die.

Therefore, "tighten his belt" is the most appropriate idiom to replace the underlined segment.