Question

Amanda and Stephen wrote the following proofs to prove that vertical angles are congruent. Who is correct?

Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles.

Amanda's Proof


Statement Justification
∠1 + ∠4 = 180° Definition of Supplementary Angles
∠3 + ∠4 = 180° Definition of Supplementary Angles
∠1 + ∠4 = ∠3 + ∠4 Transitive Property of Equality
∠1 ≅ ∠3 Subtraction Property of Equality

Stephen's Proof

Statement Justification
∠1 + ∠2 = 180° Definition of Supplementary
∠2 + ∠3 = 180°

Answer 1

Stephen's Proof is probably correct

Answer 2

What about amandas?

Answer 3

@Kash_TheSmartGuy