Question

Complete the proof....

Answer 1

Answer:

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.