Answer:
2. Definition of linear pair; 3. Angles in a linear pair are supplementary; 4. Definition of supplementary; 5. m∠1+m∠2+m∠3 = 180°; 6. Substitution; 7. m∠1+m∠2 = m∠4, substitution property of equality
Step-by-step explanation:
A linear pair is two angles that together form a straight line. ∠3 and ∠4 together form a straight line, so they are a linear pair.
The angles in a linear pair are supplementary. This means that ∠3 and ∠4 are supplementary.
Supplementary angles sum to 180°; this means that m∠3+m∠4 = 180°.
The Triangle Sum Theorem states that the three angles of a triangle have measures that sum to 180°. This means that m∠1+m∠2+m∠3 = 180°.
Substituting m∠3+m∠4 for 180° gives us m∠1+m∠2+m∠3 = m∠3+m∠4.
Subtracting m∠3 from each side, using the substitution property of equality, gives us
m∠1+m∠2 = m∠4.
