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 GivenNext box: 3x = 5x - 20 has reason Distributive PropertyNext box: -2x = -20 or maybe 3x - 5x = 5x - 20 - 5xReason 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 degreesmR = 30 degreesShow PSQ = 75 degreesProof.mSQR = 45 degrees GivenmR = 30 degrees GivenmR + mQRS + mSQR = 180 degrees Triangle Angle Sum TheoremmQSR + mPSQ = 180 degree Linear Pairs are Supplementary TheoremmQSR + mPSQ = mR + mQRS + mSQR Transitivity of equalitymPSQ = mR + mSQR Subtraction Property of EqualitymPSQ = 30 degrees + 45 degrees SubstitutionmPSQ = 75 degrees SimplificationThis isn't making geometry any better. It's just making algebra worse.3.mA1 = 35 degrees GivenmA1 + mA2 = 180 degrees Linear Pairs of SupplementarymA2 = 180 degrees - mA1 Subtraction Prop...mA2 = 180 degrees - 35 degrees SubstitutionmA2 = 145 degreesA2 is obtuse Definition of obtuse (measure > 90 degrees)