Answer:
Complete proof is shown below.
Step-by-step explanation:
Given information: [tex]\angle 2\cong \angle 4[/tex] and ∠2 and ∠3 are supplementary angles.
To prove : [tex]\angle 1\cong \angle 3[/tex]
Proof:
Statement Reason
1. ∠2 ≅ ∠4 1. Given
2. m∠2 = m∠4 2. Angle congruence postulate
3. ∠2 and ∠3 are supplementary angles 3. Given
4. m∠2 + m∠3 = 180° 4. Definition of supplementary angles
5. ∠1 and ∠4 are supplementary angles 5. Linear pairs
6. m∠1 + m∠4 = 180° 6. Definition of supplementary angles
7. m∠1 + m∠4 = m∠2 + m∠3 7. Substitution property of equality
8. m∠1 + m∠4 = m∠4 + m∠3 8. Substitution property of equality
9. m∠1 = m∠3 9. Subtraction property of equality
10. m∠1 ≅ m∠3 10. Angle congruence postulate
