∠7 ≅ ∠5     Vertical angles are congruent

 ∠1 ≅ ∠3     Vertical angles are congruent

 ∠3 ≅ ∠5     Alternate interior angles formed by parallel lines are congruent  

 ∠1 ≅ ∠5     Transitive property

 ∠1 ≅ ∠7     Transitive property



Done, probably could be done in fewer steps      

  

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