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

9º

11º

79º

38º

27º

63º

40º

102º

50º

you are here 4 9

only acute angles can be complementary

46º

52º

44º

9º

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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