Select the most appropriate option to substitute the underlined segment in the given sentence.

Rajan’s caused extremely painful headaches.

The correct option is excruciating.

Explanation:
The given sentence is: "Rajan’s caused extremely painful headaches."
We need to select the most appropriate single word to substitute the underlined phrase extremely painful.

Let's analyze the meanings of the given options:
1. excruciating: Intensely painful, severe, or agonizing. This is the exact synonym and single-word substitution for "extremely painful".
2. horrible: Very unpleasant, shocking, or disagreeable, but it does not specifically describe severe physical pain.
3. extreme: Reaching a high or highest degree, but it is an adjective indicating degree rather than specifically defining pain.
4. devastating: Causing severe shock, grief, or destruction.

Therefore, excruciating is the most appropriate word to replace extremely painful.