Use the image to answer the question.

Question

A vertical line is intersected by two parallel lines m and n forming eight angles.

Huy is working on a proof that consecutive interior angles are supplementary.

Statement Reason
1. m∠A+m∠C=180°
Linear pairs are supplementary
2. m∠A=m∠E

3. m∠E+m∠C=180°
Substitution
4. ∠E
and ∠C
are supplementary Definition of supplementary angles

What is the missing reason in the proof?

(1 point)
Responses

Vertical Angles Theorem
Vertical Angles Theorem

Transitive Property of Equality
Transitive Property of Equality

Corresponding Angles Postulate
Corresponding Angles Postulate

Definition of congruence
Definition of congruence

Answer 1

The missing reason in the proof is:

Transitive Property of Equality

This is the reasoning that connects statements 1, 2, and 3. Since \( m∠A + m∠C = 180° \) (statement 1) and \( m∠A = m∠E \) (statement 2), it follows by the transitive property that \( m∠E + m∠C = 180° \) (statement 3).