Answer:
From
m∠1 = m∠4
m∠1 + m∠2 = m∠3 + m∠4
m∠2 = m∠3 Identity property
∠2 ≅ ∠3 Equal angles are congruent
Step-by-step explanation:
Given Reason
∠1 and ∠2 are supplementary Given
Therefore;
m∠1 + m∠2 = 180° Supplementary ∠s sum up to 180°
∠3 and ∠4 are supplementary Given
Therefore;
m∠3 + m∠4 = 180° Supplementary ∠s sum up to 180°
From which we have;
m∠1 + m∠2 = 180° = m∠3 + m∠4 Transitive property
m∠1 + m∠2 = m∠3 + m∠4
∠1 ≅ ∠4 Given
m∠1 = m∠4 Congruent ∠s have equal measure
Therefore;
m∠1 + m∠2 = m∠3 + m∠1 Transitive property
Therefore;
m∠1 + m∠2 - m∠1= m∠3 + m∠1 - m∠1 Subtraction property
m∠1 - m∠1 + m∠2 = m∠3 + m∠1 - m∠1
0 + m∠2 = m∠3 + 0 Inverse property
Therefore;
m∠2 = m∠3 Identity property
∠2 ≅ ∠3 Equal angles are congruent.