SOLUTION: Given: angle 1 is congruent to angle 2; angle 1 and angle 2 are supplementary Prove: angle 1 and angle 2 are both right angles

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Question 998429: Given: angle 1 is congruent to angle 2; angle 1 and angle 2 are supplementary
Prove: angle 1 and angle 2 are both right angles
Answer by MathLover1(20849) About Me  (Show Source):
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Given: <1 and <2 and congruent; <1 and <2 are supplementary

Prove: <1 is a right angle and <2 is a right angle

Statements ---------------- Reasons

1)
<1 and <2 are congruent
<1 and <2 are supplementary---------------- given
2) m<1 = m<2 ---------------- Def of congruent angles
3) m<1 + m<2 = 180 ---------------- Def of supplementary angles
4) m<2 + m<2 = 180 ---------------- Substitution
5) 2 (m<2) = 180---------------- Combine like terms or Distributive Property
6) m<2 = 90 ---------------- Multiplication/Division Property
7) m<1 = 90 ---------------- Substitution or Transitive Property
8) <1 is a right <; <2 is a right < ---------------- Def of right angle