Why do complementary and supplementary angles not have to be adjacent?

As long as the two angles equal 90 degree then they will be complementary. As far as supplementary, as long as the two angle sum equals 180 degrees then they will be supplemental.

been there, done that.

http://www.jiskha.com/display.cgi?id=1444251037

Complementary angles and supplementary angles do not have to be adjacent because their definitions are based on the measures of the angles, rather than the positions or arrangement of the angles.

Complementary angles are any two angles that add up to 90 degrees. For example, if you have an angle measuring 30 degrees, its complementary angle would be 60 degrees. These angles could be adjacent (meaning they share a common vertex and side) or they could be separated by other angles or objects. As long as their measures add up to 90 degrees, they are complementary.

Supplementary angles, on the other hand, are any two angles whose measures sum up to 180 degrees. For instance, if you have an angle measuring 60 degrees, its supplementary angle would be 120 degrees. Just like complementary angles, supplementary angles can be adjacent or non-adjacent. As long as their measures add up to 180 degrees, they are supplementary.

It is important to note that adjacency is not a requirement for angles to be complementary or supplementary. The focus is on their measures and the relationship between the sum of those measures and the specific angle properties.