We are given that angle 1 and angle 2 are supplements, angle 3 and angle 4 are supplements, and angle 1 is congruent to angle 4.

We are asked to prove that angle 2 is congruent to angle 3.

`/_1 "supplement"/_2` Given

`m/_1+m/_2=180` Definition of supp. angles

`/_3"supplement" /_4` Given

`m/_3+m/_4=180` Definition of supp angles

`m/_1+m/_2=m/_3+m/_4` Substitution

`/_1 cong /_4` Given

`m/_1=m/_4` Definition of congruent

`m/_2=m/_3` Subtraction property of equality

`/_2 cong /_3` Definition of congruent

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