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Head First 2D Geometry by Dawn Griffiths, Stray

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18º + 72º = 90º
so these angles ar
e
complementary.
They’r
e still
complementary, ev
en if
they’r
e apart.
(And they’r
e
complimentary, t
oo!)
finding missing angles
Complementary angles always
add up to a right angle (90º)
If two angles combine to creat a right angle we call them
complementary angles. Usually, complementary angles are adjacent
(next to each other), but they can be any two angles anywhere that
add up to 90 degrees.
We say that the angles complement each other.
Hey, you look nice
today!
Thanks! Not
so bad yourself....
72º
18º “complements” 72º.
18º
72º
18º
Draw lines to connect up five pairs of complementary angles.
You’ll have two lonely single angles left over. Can you work out their complements?
Hint: Your second answer might be surprising.
46º
52º
44º
11º
79º
38º
27º
63º
40º
102º
50º
you are here 4 9
only acute angles can be complementary
46º
52º
44º
11º
79º
38º
27º
63º
40º
102º
50º
Draw lines to connect up five pairs of complementary angles.
You’ll have two lonely single angles left over. Can you work out their complements?
46º + 44º = 90º
52º + 38º = 90º
40º + 50º = 90º
79º + 11º = 90º
63º + 27º = 90º
This angle doesn’t have a
complement because it is
already bigger than 90º!
90º - 9º = 81º, so the complement
of this angle would be 81º.
Did this sur
pr
ise you?
Q:
How can I tell which angles do and
don’t have a complement?
A:Only acute angles—angles less than
90º—can be complementary. An obtuse
angle is already greater than 90º on its own.
Q:
Why doesn’t 102º have a negative
complement of –12º? Surely that would
add up to 90º?
A:Complements can never be negative.
There’s no real reason for this except that the
term “complementary” means two positive
angles which add up to 90º.
Only acute
angles can be
complementary.
10 Chapter 1

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