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A supplement of an angle is the angle that we add to the initial angle and have a result of 180 degrees. The supplement of 31 degrees is 180-31=149 degrees.
Complementary angles consist of 2 angles that add up to 90 degrees; so the complimentary angle to a 31 degree angle is a 59 degree angle.
A pair of supplementary angles add up to 180 degrees. Therefore, the supplement to a 149 degree angle is equal to 180 - 149 = 31 degrees.
Suppose the larger angle is x degrees. Then the smaller angle is x - 2 degrees, and so they sum to 2x - 28 degrees. The two angles are complementary, so 2x - 28 = 90 is 2x = 90 + 28 = 118 so that x = 118/2 = 59 degrees and then x - 29 = 59 - 28 = 31 degrees. The two angles are 59 and 31 degrees.
The supplement of an angle is the angle that, when added to the original angle, equals 180 degrees. The complement of an angle is the angle that, when added to the original angle, equals 90 degrees. Therefore, the supplement of the complement of a 38-degree angle would be the angle that, when added to the complement of 38 degrees (52 degrees), equals 180 degrees. This angle would be 128 degrees.