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The complete proof statement and reason for the required proof is as follows:

Statement                                    Reason

m<PNO = 45                               Given

MO                                              Given

<MNP and <PNO are a
linear pair of angles                     Definition of linear pairs of angles

<MNP and <PNO are
supplementary angles                 Linear Pair Postulate

m<MNP + m<PNO = 180°          Definition of supplementary angles

m<MNP + 45° = 180°                 Substitution property of equality

m<MNP = 135°                          Subtraction property of equality

Answer:

Definition of Linear Pairs of Angles; and Definition of supplementary angles.

Step-by-step explanation:

A linear pair is two angles that form a straight line.  Thus our second step, that ∠MNP and ∠PNO are a linear pair, is from the definition of linear pairs.

We know from our third step that linear pairs are supplementary.  By the definition of supplementary angles, this means they have a sum of 180°.

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