Given: m∠1=115°, m∠2=65°Prove: m∥nMatch the reason for each statement in order to complete the proof. The statements are listed in order. A reason may be used once, more than once, or not at all.(2 points)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.m∠1=115°, m∠2=65°115°+65°=180° m∠1+m∠2=180°∠1 and ∠2 are supplementary.m∥n SubstitutionDefinition of supplementary anglesConsecutive Interior Angles Converse TheoremGivenCorresponding Angles Converse PostulateAdditionTransitive Property of CongruenceDefinition of vertical angles

Answer 1

To complete the proof that lines m and n are parallel (m∥n) given that m∠1 = 115° and m∠2 = 65°, we will organize the statements with the appropriate reasons from your provided list. Here's how the steps can be laid out:

1. Statement: m∠1 = 115°,
   Reason: Given.

2. Statement: m∠2 = 65°,
   Reason: Given.

3. Statement: 115° + 65° = 180°,
   Reason: Addition.

4. Statement: m∠1 + m∠2 = 180°,
   Reason: Substitution.

5. Statement: ∠1 and ∠2 are supplementary,
   Reason: Definition of supplementary angles.

6. Statement: m∥n,
   Reason: Consecutive Interior Angles Converse Theorem.

So, filling in the correct responses:

1. Given
2. Given
3. Addition
4. Substitution
5. Definition of supplementary angles
6. Consecutive Interior Angles Converse Theorem

This structure demonstrates that since angles 1 and 2 are supplementary, lines m and n must be parallel according to the theorem concerning consecutive interior angles.