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.)
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
