SOLUTION: complements of congruent angles are congruent ..

Question 664899: complements of congruent angles are congruent ..
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Complementary angles are two angles that add up to 90�.
the theorems listed here for complementary angles:
Complements of the same angle are congruent. If two angles are each complementary to a third angle, then they�re congruent to each other. (Note that this theorem involves three total angles.)
Complements of congruent angles are congruent. If two angles are complementary to two other congruent angles, then they�re congruent. (This theorem involves four total angles.)

W3C Web site

The logic shown in these two figures works the same when you don�t know the size of the given angles
proof:
complements of congruent angles are congruent
<1 and <2 complements , <1 and <3 complements.........given
m<1 +m<2 =90�, m <1 +m<3 =90�,.......definition of complementary angles
m<1 +m<2 =m <1 +m<3..........................transitive property of equality
m<2 =m<3.............................................subtraction property of equality
m<=~ m<..................................definition of congruent angles

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