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Petit, a 31-year-old utility man who has played parts of five seasons in the Major Leagues over the past nine years, slashed .245/.299/.348 with 13 doubles and 20 runs scored in 204 at-bats over 89 games for the Angels in 2016. Ege, a 25-year-old left-hander, pitched in 13 games for the Angels last season, compiling a 1.04 ERA and striking out nine batters in 8 2/3 innings.
The Angels have a full 40-man roster heading into Monday's Winter Meetings.
MLB.com and MLB Network will have wall-to-wall coverage of the 2016 Winter Meetings from the Gaylord National Resort & Convention Center outside Washington, D.C. Fans can watch live streaming of all news conferences and manager availability on MLB.com, including the Rule 5 Draft on Thursday at 6 a.m. PT.
Doug Miller is a reporter for MLB.com. Follow him on Twitter @DougMillerMLB. This story was not subject to the approval of Major League Baseball or its clubs.