Explain what it means to say that two angles are complementary and that two are supplementary. Can complementary angles be adjacent?

Question

Explain what it means to say that two angles are complementary and that two are supplementary. Can complementary angles be adjacent? Can they be vertical? Can supplementary angles be adjacent? Can they be vertical? Give examples of each type.

Answer 1

Complementary angles add up to 90

Supplementary angles add up to 180

YES, complementary angles can be adjacent. (1)

YES, complementary angles can be vertical only if they

measure exactly 45 degrees each (2)

YES, supplementary angles can be adjacent. (3)

YES, supplementary angles can be vertical only if they

measure exactly 90 degrees each. (4)

I have uploaded the diagram for you in the RESOURCES section.

You MUST download the diagram and open it up so you can

understand what is going on!

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Here is the construction that illustrates the 4 examples.

Horizontal line on the x-axis at y=0, and vertical

line on the y-axis at x=0.

Angle C is the right angle on the NORTHWEST corner in

quadrant 2.

Stray line bisects passing northeast to southwest bisects

the right angles in quadrants 1 and 3, forming angles A and B

in quadrant 1, Such that A=45, which forces B=45.

So starting with the the positive y-axis at the NORTH, the

angles in CLOCKWISE order, are A,B,F,E,D,C, where

C is the right angle in quadrant 2 and A=B=45 in quadrant 1.

See the refer to the uploaded diagram.

Answer 2