Measure angle 1 plus measure angle 2 = 180 by definition of supplementary.
Measure angle 1 greater than 90 by definition of obtuse.
Measure angle 2 = 180 minus measure angle 1 by addition postulate
If measure angle 1 is greater than 90, then measure angle 1 must be equal to 90 plus some real number x where x is greater than zero. Definition of "greater than"
Measure angle 2 = 180 - (90 + x) = 90 - x where x > 0. By substitution and the distributive property.
Measure angle 2 is less than 90 by definition of "less than"
Angle 2 is acute by definition of acute.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
