Question

given: ∠2≅∠3; ∠1 and ∠2 form a linear pair. prove: ∠1 and ∠3 are supplementary. statements reasons 1. ∠2≅∠3 1. 2. m∠2 = m∠3 2. 3. ∠1 and ∠2 form a linear pair 3. 4. ∠1 and ∠2 are supplementary 4. 5. m∠1 + m∠2 = 180° 5. 6. m∠1 + m∠3 = 180° 6. 7. ∠1 and ∠3 are supplementary 7.

Explanation:

Step1: Given information

Given

Step2: Definition of congruent angles

Definition of congruent - angles (if two angles are congruent, their measures are equal)

Step3: Given information

Given

Step4: Linear - pair postulate

If two angles form a linear pair, they are supplementary

Step5: Definition of supplementary angles

Definition of supplementary angles (the sum of the measures of supplementary angles is 180°)

Step6: Substitution property of equality

Since \(m\angle2 = m\angle3\), substitute \(m\angle3\) for \(m\angle2\) in \(m\angle1 + m\angle2=180^{\circ}\)

Step7: Definition of supplementary angles

Definition of supplementary angles (if the sum of the measures of two angles is 180°, the angles are supplementary)

Answer:

1. Given
2. Definition of congruent angles
3. Given
4. Linear - pair postulate
5. Definition of supplementary angles
6. Substitution property of equality
7. Definition of supplementary angles