Most of the people fail to understand the difference between complementary angles and supplementary angles and mix both of these terms. No doubt the difference between both terms is very marginal and the remaining features of these terms mostly look alike. This is the main reason why people have been confusing both of these terms with each other and using them interchangeably on frequent basis.
Most of the geometry questions revolve around angles and arcs, therefore it is of utmost importance that one should learn the difference well. Complementary angles are those angles which when added together, form a right angle. The right angle is an angle which forms a straight vertical line and is primarily associated with the angle of 90 degrees. Furthermore, all those angles which when summed up together produce the result of 90 degrees are called complementary angles.
On the other hand, when the sum of two angles is equal to 180 degrees, both of these angles are called supplementary angles. Supplementary angles, when added together, form a straight horizontal line that is equivalent to the angle of 180 degrees. Unlike other angles and terms, it is not important that both of these angles should be together. For example, if we take two different angles of two separate triangles and the sum of these appears to be 90 degrees or 180 degrees, these angles will be called complementary or supplementary angles respectively.
Note that if the sum of two angles is not exactly equal to 90 or 180 degrees then the angles are not complementary or supplementary. It is of utmost importance that the sum should be exactly equal to these figures. For instance, the angles of 30 and 60 degrees are called complementary angles because 30 + 60 = 90. Similarly, the sum of 35 and 145 is equal to 180 and both of these angles are called supplementary.