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to turn away (one's eyes, face, etc.); to avert; to divert (e.g. one's attention); to evade (e.g. a question); to change (e.g. the subject)
to displease; to annoy; to offend; to upset
to miss (the target, ball, etc.)
彼女は目をそらして質問に答えなかった。
She averted her eyes and didn't answer the question.
話題をそらして核心に触れないようにした。
I changed the subject to avoid touching on the core issue.
恥ずかしくて彼の視線から目をそらした。
I was embarrassed and looked away from his gaze.