Complementary and Supplementary angles are two types of pairs of angles that appear throughout geometry. Angles are complementary if all of their measures add up to 90 degrees, or a right angle. A pair of angles are supplementary if all of their measures add up to 180 degrees, or a straight line. Simply put, any pairs of angles that are formed by breaking up a right angle are complementary, and any angles that are formed by breaking up a straight line with one point are supplementary.

## Examples of Complimentary and Supplementary Angles

Review the angles below.

We know that angles A and B are compleentary because they are formed by breaking up a right angle into two angles. Similarly, we know that angles G and I are supplementary because they are formed by breaking up a straight line froma single point. Angles H and K are NOT supplementary, though, because they do not split at the same point, even though H and I along with the pair of J and K are supplementary. C and E are complementary, because 40+50=90 degrees, just like D and F are complementary since 60+30=90 degrees.

## The uses of complementary and supplementary angles

Even though complementary angles do not see much use in geometry, Supplementary angles are used all the time. For instance, you often use the rules of supplementary angles to find the otehr angles in the pattern created by a transversial. They are also used for finding the measure of the exterior angles of a polygon, or in many cases as parts of various “fill-in-the-measure” diagrams seen so often in textbooks.

Above, we see a diagram of a standard transversial of two parallel lines. Each of the red lines marks a pair of supplementary angles, and because of this and the properties of parallel lines, all you need is one measure of one angle to find all of the others. Without the rules of supplementary angles, this would not be possible!

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