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Rhame, 27, was limited to 6 1/3 innings in the majors and 20 2/3 innings in the minors last season due to an elbow issue. He underwent ulnar nerve transposition surgery in mid-August.
Though Rhame has a career 6.23 ERA in the big leagues, he showed promise at Triple-A from 2016-18, averaging better than 10 strikeouts per nine innings in all three years. The Angels are taking a flier on the right-hander to see if he can translate that success to the majors.