Subject: supplementary angles

Name: Suzanne
Who is asking: Teacher
Level: Middle

Question:
We know that: Supplementary angles are two angles whose sum equals 180 degrees and complementary angles are two angles whose sum equals 90 degrees. Are supplementary and complementary angles necessarily adjacent? or can they be non-adjacent?

Thanks for clearing this up!

You have the definitions correct: the angles do not have to share the same vertex; they can be anywhere in the plane. If A + B = 180 degrees the pair is called "supplementary", with A the supplement of B and B the supplement of A. For example, if A, B, C, D are four points lying on a circle in the given order, then a theorem of Euclid says that A and C are supplementary angles.

When A + B = 90 degrees the pair is called "complementary", with A the complement of B and B the complement of A.