Angles 1,2,3 and 4 are formed by two intersecting lines. State the single angle fact necessary to prove that m<1+m<2=m<2+m<3

The angle fact that is necessary to prove that m∠1 + m∠2 = m∠2 + m∠3 is: linear pair are supplementary.
Thus,
∠1 and ∠2 are on a straight line, therefore,
m∠1 + m∠2 = 180°
∠2 and ∠3 are on a straight line, therefore,
m∠2 + m∠3 = 180°
Thus:
m∠1 + m∠2 = m∠2 + m∠3
Therefore, the angle fact that is necessary to prove that m∠1 + m∠2 = m∠2 + m∠3 is: linear pair are supplementary.
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