Complete the proof.

The correct options are;

1. Definition of supplementary angles

2. m∠1 + m∠2 = m∠1 + m∠3

3. m∠2 = m∠3

4. Definition of Congruent Angles

Step-by-step explanation:

The two column proof is presented as follows;

Statement                                            Reason

1. ∠1 and ∠2 are supplementary         Given

  ∠1 and ∠3 are supplementary

2. m∠1 + m∠2 = 180°                            Definition of supplementary angles

  m∠1 + m∠3 = 180°

3. m∠1 + m∠2 = m∠1 + m∠3                Transitive Property

4. m∠2 = m∠3                                     Subtraction Property of Equality

5. ∠2 ≅ ∠3                                          Definition of Congruent Angles

Given that angles ∠1 and ∠2 are supplementary angles and angles ∠1 and ∠3 are are also supplementary angles, then the sums of m∠1 + m∠2 and m∠1 + m∠3 are equal, therefore, ∠2 and ∠3 have equal quantitative value and therefore ∠2 = ∠3 and by definition, ∠2 ≅ ∠3.

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