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Complementary and supplementary angles


Before we define what we mean by complementary and supplementary angles, here is an important reminder about adjacent angles


Adjacent angles: Angles that share a vertex and a common side



Complementary angles:

Two angles whose measures add to 90 degrees. It is easy to see when the angles are adjacent like the following:

complementary-angles-image

Angles x and y are adjacent because they share a ray (line in black) and a vertex (point in black called D).

Now why are they complementary?

Notice also that the angle in blue measures 90 degrees

Since the measure of angle x plus the measure of angle y = 90 degrees, x and y are complementary

Angles do not have to be adjacent to be complementary. The following angles are also complementary as long as the sum of the measures equal 90 degrees

complementary-angles-image

Supplementary angles:

Two angles whose measures add to 180 degrees. It is easy too to see this when the angles are adjacent like the following:

complementary-angles-image

Again, angles a and b adjacent because they share a ray (line in black) and a vertex (point in black called D), so they are adjacent angles.

Now why are they supplementary?

Notice also that the angle in blue measures 180 degrees because the angle is a striaght line and a straight line measures 180 degrees

Since the measure of angle a plus the measure of angle b = 180 degrees, a and b are supplementary

Again, angles do not have to be adjacent to be supplementary. The following angles are also supplementary as long as the sum of the measures equal 180 degrees

complementary-angles-image

Here we go! Study the types of angles carefully. This is where any serious study of geometry begin.




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