Short Answers (see section below this one for further explanation):
Reason 2: Same Side Interior Angle Theorem
Reason 3: Definition of Supplementary
Reason 5: Definition of Congruence
Reason 7: Definition of Supplementary
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Step-by-step explanation:
Reason 2: The "Same Side Interior Angle Theorem" is the idea that if we know two lines are parallel, then the interior angles on the same side of the transversal line will be supplementary (add to 180 degrees). In other words, the two angles can be combined to form a straight angle
Reason 3: If we're told two angles are supplementary, then by definition it means they add to 180 degrees.
Reason 5: If two angles are congruent, then they have the same measure (eg: both are 60 degrees)
Reason 7: This is the reverse of reason 3, more or less. If we know two angles add to 180 degrees then we can say they are supplementary. When it comes to definitions we can reverse it (i.e, if P, then Q reverses to if Q then P)