Easy geometry! easy geometry! easy geometry!

Answers:

b. Linear Pair
c. Definition of supplementary
d. Substitution; Combine like terms
e. Division Property of Equality
f.  Definition of Right Angle
g. Definition of Perpendicular


Further Explanations:

b. A linear pair is simply a result of cutting a straight angle into two pieces. They are adjacent and supplementary (add to 180 degrees)

c. If two angles are supplementary then they add to 180. This is simply a definition to memorize. 

d. The "m < 2" is replaced with "m < 1" through the substitution property. This is possible because of statement (a) on the first line of the proof. The teacher has also combined like terms. Technically this step would require its own line. 

e. Think of this as 2x = 180 solving to x = 90. The step done here is dividing both sides by 2, which uses the division property of equality. Alternatively you can use the multiplication property of equality to multiply both sides by 1/2 = 0.5

f. If an angle is 90 degrees, then by definition it is considered a right angle. This is another thing you memorize.

g. Also to be memorized is the fact that if two segments form a right angle, then they are considered perpendicular segments. The upside down T symbol means "perpendicular to"