Here's why:
* Adjectives modify nouns: They tell us more about the noun they describe. For example, "the red car."
* Adverbs modify verbs, adjectives, or other adverbs: They tell us more about the action, quality, or manner of something. For example, "He walked slowly."
In the sentence "He was somewhat tired," "somewhat" modifies the adjective "tired," indicating the degree of tiredness.