SOLUTION: If angles 1 and 2 are supplementary, and angle 1 is obtuse, prove angle 2 is acute.
Algebra.Com
Question 811964: If angles 1 and 2 are supplementary, and angle 1 is obtuse, prove angle 2 is acute.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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
RELATED QUESTIONS
The sum of the measures of two angles is 120 degrees .If the measure of one of the angles (answered by rapaljer)
Given: angle 1 is congruent to angle 2; angle 1 and angle 2 are supplementary
Prove:... (answered by MathLover1)
Given: angle 1 is obtuse and angle 2 is acute.
Prove: angle 1 is congruent to angle 2.... (answered by fractalier)
Given: Angle 1 is congruent to angle 3
Prove: angle 2 and angle 3 are supplementary (answered by Alan3354)
1.If two angles are supplementary and one is acute the other is obtuse, 2.If tow angles... (answered by stanbon)
Given: angle 2 and 4 are supplementary
Prove: angle 1 is congruent to angle... (answered by ikleyn)
Given: angle 2 is congruent to angle 3, angle 1 and 2 are supplementary
Prove: angle 1... (answered by Theo)
If angle 1 and angle 2 are supplementary angles and angle 1 is 12 more than angle 2, what (answered by tommyt3rd)
If angle 1 and angle 2 are supplementary angles and angle 1 is 12 degrees more than angle (answered by stanbon)
