The first blank would be the Corresponding Angles Postulate because corresponding angles are congruent
The second blank would be the Supplementary Angles Theorem because it states that if two angles share one a common line, they are supplements and add to 180
If angle 1=120 that means that angle 5 must also equal 120 and because angle 5 and 6 are on the same line their sum must be 180. 180-120=60 so that proves angle 6=60
