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Given: angle 1 and angle 2 form a linear pair; angle 2 is congruent to angle 4 Prove: angle 1 and angle 3 are supplementary

Given angle 1 and angle 2 form a linear pair angle 2 is congruent to angle 4 Prove angle 1 and angle 3 are supplementary class=

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Answer:

Step-by-step explanation:

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

olayemiolakunle65

Supplementary angles are two or more angles that add up to [tex]180^{o}[/tex]. Thus < 1 and < 3 are supplementary due to the supplementary angles addition theorem.

When two or more angles add up to form [tex]180^{o}[/tex], then they are supplementary. So that applying the required angles postulates or theorems, the following reasons can be deduced:        

 Statements                                       Reasons

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

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

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

4. ∠2 = ∠4                                          Given  

5. ∠3 = ∠4                                          Vertical opposite angle Postulate  

6. ∠2 = ∠3                                          Corresponding angle theorem  

7. m∠2 = m∠3                                    Corresponding angles are congruent  

8. m∠1 + m∠3 = [tex]180^{o}[/tex]                          Supplementary angle Postulate

9.  <1 and <3 are Supplementary     Supplementary angles addition theorem

Therefore <1 and <3 are supplementary angles because they add up to [tex]180^{o}[/tex].

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