The reason for step 4 that is missing is: definition of linear pair.
What is a Linear Pair of a Straight Line Angle?
A line pair are two angles on a straight line whose sum equals 180 degrees.
Angles ANV and ANR line on a straight line and are therefore linear pair. This implies that:
m∠ANV + m∠ANR = 180 degrees
Therefore, the missing reason is: definition of linear pair.
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