By the time I had reached the bottom of the mountain, I ____ extremely tired.

Explanation of all the options:

1.feel

• Explanation: "Feel" is in the present tense, which does not fit the past context of the sentence. The sentence describes a situation that happened after reaching the bottom of the mountain.
• Incorrect ❌

2.have felt

• Explanation: "Have felt" is in the present perfect tense, which is used for actions that occurred at an unspecified time in the past and have relevance to the present. This does not fit the context of the sentence, which is clearly past.
• Incorrect ❌

3.was feeling

• Explanation: "Was feeling" is in the past continuous tense. While this could potentially fit, it implies an ongoing action rather than a completed feeling at a specific point in the past, making it less suitable than option 5.
• Incorrect ❌

4.an feeling

• Explanation: "An feeling" is grammatically incorrect. "Feeling" cannot be preceded by "an" in this context, making this option invalid.
• Incorrect ❌

5.felt

• Explanation: "Felt" is the simple past tense of "feel," which fits perfectly in the sentence. It indicates a completed action that occurred after reaching the bottom of the mountain.
• Correct ✅