Angle 1 and angle 2 are a linear pair; angle 1 and 3 are vertical angles. Prove angle 2 and angle 3 are a linear pair

Question

I need a answer as soon as possible. Please solve in six steps

Answer 1

Statements                                                    Reasons                                    

1. ∠1 and ∠2 are a linear pair                          1. Given

2. ∠1 and ∠2 are supplementary                      2. Linear Pair Postulate

3. m∠1 + m∠2 = 180°                                    3. Definition of Supplementary Angles

4. ∠1 and ∠3 are vertical angles                      4. Given

5. ∠1 ≅ ∠3                                                     5. Vertical angles are congruent.

6. m∠1 = m∠3                                               6. Congruent angles have equal measure.

7. m∠3 + m∠2 = 180º                                    7. Substitution into step 3.

8. ∴∠2 and ∠3 are supplementary                    8. Definition of Supplementary Angles

 

Sorry, I got 8 steps. Perhaps, you can eliminate two of my steps. I'm used to showing every little thing. :)