I'd like to throttle the educator who's harebrained idea it was to use geometry class to ruin algebra.
1.
The first reason in these two column proofs is always Given
Next box: 3x = 5x - 20 has reason Distributive Property
Next box: -2x = -20 or maybe 3x - 5x = 5x - 20 - 5x
Reason for next step x=10. I suppose we'd call this the Division Property of Equality because we divided both sides of an equation by -2.
2.
mSQR = 45 degrees
mR = 30 degrees
Show PSQ = 75 degrees
Proof.
mSQR = 45 degrees Given
mR = 30 degrees Given
mR + mQRS + mSQR = 180 degrees Triangle Angle Sum Theorem
mQSR + mPSQ = 180 degree Linear Pairs are Supplementary Theorem
mQSR + mPSQ = mR + mQRS + mSQR Transitivity of equality
mPSQ = mR + mSQR Subtraction Property of Equality
mPSQ = 30 degrees + 45 degrees Substitution
mPSQ = 75 degrees Simplification
This isn't making geometry any better. It's just making algebra worse.
3.
mA1 = 35 degrees Given
mA1 + mA2 = 180 degrees Linear Pairs of Supplementary
mA2 = 180 degrees - mA1 Subtraction Prop...
mA2 = 180 degrees - 35 degrees Substitution
mA2 = 145 degrees
A2 is obtuse Definition of obtuse (measure > 90 degrees)
