1. He drove his car carefully.
2. He drove his car in a careful manner/way.
3. He greeted the person politely.
4. He greeted the person in a polite manner/way.
5. He said no angrily.
6. He said no in an angry manner/way.
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Is each pair interchangeable?
Yes, but the sentences with the adverbs are better -- shorter, more concise.
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Yes, each pair in the given examples is interchangeable. In each case, the first sentence provides a statement about an action or behavior, while the second sentence provides an alternative way to express the same idea by using an adverb and a noun phrase ("in a + adjective + manner/way").
The adverb modifies the verb to indicate the speaker's attitude or approach, while the adjective in the noun phrase describes the manner in which the action or behavior is performed. Both sentences convey the same meaning, but the second sentence in each pair provides a more explicit description of how the action or behavior is carried out.