Complete the proof of the exterior angle theorem. given: ∠4 is an exterior angle of △abc. prove: m∠1+m∠2=m∠4 statement reason 1. ∠4 is an exterior angle of △abc. 1. 2. ∠3 and ∠4 form a linear pair. 2. 3. ∠3 is supplementary to ∠4. 3. 4. m∠3+m∠4=180° 4. 5. 5. triangle sum theorem 6. m∠1+m∠2+m∠3=m∠3+m∠4 6. 7. 7.

Step-by-step explanation:

Statement                                                                              Reason

1. ∠4 is an exterior angle of ΔABC                                         Given

2. ∠3 and ∠4 form a linear pair                                    Linear pair property

3. ∠3 is supplementary to ∠4                                     Straight line property

4. m∠3+m∠4=180°                                                ∠3 is supplementary to ∠4      

5. m∠1+m∠2+m∠3=180°                                           Triangle sum theorem

6.m∠1+m∠2+m∠3= m∠3+m∠4                                   Statement 4 and 5

7. m∠1+m∠2=m∠4                                                     Subtraction property

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