Question

the following proofs to prove that vertical angles are congruent. who is correct
amandas proof

statement	justification
$\angle3 + \angle4 = 180^\circ$	definition of supplementary angles
$\angle1 + \angle4 = \angle3 + \angle4$	substitution property of equality
$\angle1 \cong \angle3$	subtraction property of equality

stephens proof

statement	justification
$\angle2 + \angle3 = 180^\circ$	definition of supplementary angles
$\angle1 + \angle2 = \angle2 + \angle3$	substitution property of equality
$\angle1 \cong \angle3$	subtraction property of equality

Explanation:

Both Amanda and Stephen use valid logical steps: they first identify pairs of supplementary angles (angles forming a linear pair that sum to $180^\circ$), apply the substitution property to set the two sums equal, then use the subtraction property to eliminate the common angle and prove vertical angles $\angle1 \cong \angle3$. Their reasoning follows the standard proof for congruent vertical angles.

Answer:

Both Amanda and Stephen are correct.