Which of the following statements correctly completes the proof that consecutive interior angles are supplementary?

Question

Given: n∥m
Statements Reasons
1. m∡A+m∡C=180°
1. Linear Pairs are supplementary
2. m∡A=m∡E
2. __________________________
3.. m∡E+m∡C=180°
3. Substitution
4. ∠E and ∠C
are supplementary 4. Definition of Supplementary Angles


(1 point)
Responses

Corresponding Angles Postulate
Corresponding Angles Postulate

Vertical Angles Theorem
Vertical Angles Theorem

Definition of congruence
Definition of congruence

Transitive Property of Equality
Transitive Property of Equality
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Answer 1

To complete the proof that consecutive interior angles are supplementary, we need to find a statement and reason that connects the equation \( m∡A = m∡E \) with the given information.

Here's the completed proof with the appropriate statement and reason filled in:

Given: \( n \parallel m \)

Statements | Reasons --------------------------------------|----------------------------------------

1. \( m∡A + m∡C = 180^\circ \) | Linear pairs are supplementary
2. \( m∡A = m∡E \) | Corresponding Angles Postulate
3. \( m∡E + m∡C = 180^\circ \) | Substitution
4. ∠E and ∠C are supplementary | Definition of Supplementary Angles

So the correct response to fill in the blank is:

Corresponding Angles Postulate