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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

Definition of congruence
Definition of congruence

Vertical Angles Theorem
Vertical Angles Theorem

Transitive Property of Equality
Transitive Property of Equality

Corresponding Angles Postulate
Corresponding Angles Postulate
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Answer 1

The missing reason in the proof is:

Vertical Angles Theorem

This is because m∠A and m∠E are vertical angles, which are congruent to each other. Therefore, the reason for statement 2 (m∠A = m∠E) is the Vertical Angles Theorem.