Use the image to answer the question.

Question

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Huy is working on a proof that consecutive interior angles are supplementary.
Statement
Reason
1. m/Am/C = 180°
Linear pairs are supplementary
2. m/Am/E
3. m/E+m∠C = 180°
Substitution
4. E and ∠C are supplementary
Definition of supplementary angles

Answer 1

To analyze the proof that consecutive interior angles are supplementary, we can summarize the statements and provide clarity on the reasoning:

1. Statement: \( m\angle A + m\angle C = 180^\circ \)
   Reason: Linear pairs are supplementary

   • This establishes that angles A and C, being a linear pair, sum up to 180 degrees.

2. Statement: \( m\angle A + m\angle E \)
   Reason: Postulated or previously known angle measures

3. Statement: \( m\angle E + m\angle C = 180^\circ \)
   Reason: Substitution

   • This uses the information from step 1 and substitutes \( m\angle A \) with \( m\angle E \) if they are equal, claiming that the two angles (E and C) also sum up to 180 degrees.

4. Statement: \( \angle E \) and \( \angle C \) are supplementary
   Reason: Definition of supplementary angles

   • This statement concludes that angles E and C, summing to 180 degrees, are defined as supplementary angles.

As a whole, these statements, along with their reasoning, collectively lead to proving that consecutive interior angles (in this case, \( \angle E \) and \( \angle C \)) are indeed supplementary.

If you have specific actions you would like to take on this proof, or if you need further expansion or explanation on each step, please let me know!