Question

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 Corresponding Angles Postulate Corresponding Angles Postulate Definition of congruence Definition of congruence Transitive Property of Equality Transitive Property of Equality Vertical Angles Theorem Vertical Angles Theorem Skip to navigation

Answer 1

In the proof that consecutive interior angles are supplementary, the missing reason in the proof where \( m∠A = m∠E \) (Statement 2) is related to the relationship between parallel lines and the angles that are formed when a transversal crosses them.

The correct reason to fill in for Statement 2 is: Corresponding Angles Postulate.

Thus the completed proof would look like this:

1. \( m∠A + m∠C = 180° \) - Linear pairs are supplementary
2. \( m∠A = m∠E \) - Corresponding Angles Postulate
3. \( m∠E + m∠C = 180° \) - Substitution
4. \( ∠E \) and \( ∠C \) are supplementary - Definition of supplementary angles

So the missing reason is Corresponding Angles Postulate.