No. For example 30 and 60 degrees are complementary angles. Their supplementary partners are 150 and 120 degrees.
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if two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
Complementary angles are those that add up to 90° Thus all angles complementary to a given angle must all be the same angle (90° - the_given_angle), ie they are all congruent angles.
Congruent adjacent complementary angles are two angles of 45° that share one side and its vertex.. which means: A 90° angle divided in two halfs of 45°.
If 2 angles are congruent and complementary, they must each be 45 degrees.
Only if the congruent angle is the angle between the two congruent sides (SAS postulate).