In geometry, supplementary angles are two angles whose sum is equal to 180 degrees. This means that the angles are next to each other and form a straight line. Supplementary angles are often encountered when working with triangles, as the sum of the interior angles of a triangle is always 180 degrees.

To determine if two angles are supplementary, you can add their measures. If the sum is 180 degrees, then the angles are supplementary. For example, 45 degrees and 135 degrees are supplementary because 45 + 135 = 180.

Supplementary angles are also related to complementary angles. Complementary angles are two angles whose sum is equal to 90 degrees. If two angles are supplementary, then their complements are complementary. For example, if 45 degrees and 135 degrees are supplementary, then 45 degrees complement 135 degrees and vice versa.

Supplementary angles play an important role in geometry because they can be used to determine the measures of other angles. For example, if you know that one angle in a triangle is 60 degrees and another angle is 45 degrees, then you can conclude that the third angle must be 75 degrees because the sum of the interior angles of a triangle is always 180 degrees.