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

Transitive Property of Equality
Transitive Property of Equality

Corresponding Angles Postulate
Corresponding Angles Postulate

Definition of congruence
Definition of congruence

Vertical Angles Theorem

Answer 1

The missing reason in the proof is:

**Corresponding Angles Postulate**

This is because step 2 states that m∠A = m∠E, and since lines m and n are parallel, the angles created by the intersecting vertical line and the two parallel lines are corresponding angles, which are congruent when the lines are parallel. Thus, the correct reason for statement 2 is the Corresponding Angles Postulate.