Question 1089989: Given: <1 is congruent to <2; < 1 and <2 are supplementary.
Prove: <1 & <2 are right angles.
(picture: http://imgur.com/WxNdiTh
<1 is congruent to <2 (Given)
<1 & <2 are supplementary (Given)
m<1 = m<2 (Definition of congruent angles)
m<1 + m<2= 180 (?)
m<1 + m<1= 180 (Substitution Property)
2(m<1) = 180 (Substitution Property)
2(m<1)/2 = 180/2 (Multiplication/Division Property)
m<1 = 90 (Substitution Property)
m<2 = 90 (?)
<1 and <2 are right angles (Definition of right angles)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
If "< 1 & < 2 are supplementary" is given, then what immediately follows is that "m < 1 + m < 2 = 180" by the definition of supplementary angles. In other words, if two angles are supplementary, then they add to 180 degrees.
If m < 1 = m < 2, and m < 1 = 90, then m < 2 = 90 as well through the substitution property (or you could argue the transitive property of equality which is very similar). You can think of it as starting off with m < 1 = m < 2, then replacing the "m < 1" with "90". This replacement is valid because of m < 1 = 90.
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