The missing reasons for the given two column proof are respectively;
Reason 2; Definition of Supplementary angles
Reason 3; Substitution Property of Equality
Reason 4;Subtraction Property of Equality
From the two column proof, we are given that;
m∠2 = m∠3
Now, for m∠1 + m∠2 = 180°, we see that m∠1 and m∠2 are on a straight line and we know that angles on a straight line sum up to 180°. Thus, the reason is because they are supplementary angles.
Similarly, m∠3 and m∠4 are on a straight line and as such;
m∠3 + m∠4 = 180°
m∠1 + m∠2 = m∠3 + m∠4. This is true because of substitution property of equality.
Lastly, since m∠2 = m∠3, then it means that they will cancel out in the statement 3 and as such we now have;
m∠1 = m∠4. The reason is subtraction property of equality
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