Question

mia is working on a proof that consecutive interior angles are supplementary. two - column proof of 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)

Explanation:

Step1: Identify the relevant angles

We have two - parallel lines \(m\) and \(n\) cut by a transversal. \(\angle A\) and \(\angle C\) form a linear - pair (reason for statement 1: Linear pairs are supplementary). \(\angle A\) and \(\angle E\) are corresponding angles.

Step2: Recall the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are congruent. So, the reason for \(m\angle A=m\angle E\) is "Corresponding angles postulate".

Step3: Analyze the substitution step

Since \(m\angle A + m\angle C=180^{\circ}\) and \(m\angle A=m\angle E\), we substitute \(m\angle A\) with \(m\angle E\) to get \(m\angle E + m\angle C = 180^{\circ}\) (reason for statement 3: Substitution).

Step4: Understand the conclusion

The statement "\(\angle E\) and \(\angle C\) are supplementary" follows from the definition of supplementary angles (reason for statement 4: Definition of supplementary angles).

Answer:

The missing reason for \(m\angle A=m\angle E\) is "Corresponding angles postulate".