uy 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? A. Corresponding Angles postulate B. Vertical Angles Theorem C. Transitive property of Equality D. Definition of congruence

Answer 1

To determine the missing reason in the proof that consecutive interior angles are supplementary, let's analyze the statements provided:

1. m∠A + m∠C = 180° - This statement is correct because it says that the angles create a linear pair, which are supplementary.
2. m∠A = m∠E - This is likely based on a given or established relationship where angles A and E are congruent (which could be from the Corresponding Angles Postulate).
3. m∠E + m∠C = 180° - This is reached by substitution; since m∠A = m∠E, they can be substituted into the first statement about supplementary angles.
4. ∠E and ∠C are supplementary - This statement concludes that angles E and C add up to 180°, confirming that they are supplementary.

Given the context, the missing reason for step 3 (which states the relationship of m∠E and m∠C being 180°) would relate to the equality established in step 2 and the initial hypothesis of angles A and C (step 1).

The logical connection would be best explained by the Transitive Property of Equality, which states that if two angles are both equal to a third angle, then they are equal to each other. Therefore, if m∠A = m∠E and m∠A + m∠C = 180°, then through substitution, it leads to m∠E + m∠C = 180°.

Hence, the missing reason in the proof is:

C. Transitive Property of Equality.