Download types of angles and naming angles

measurement anD Geometry • geometriC reasoning
2. To construct an angle that is larger than 180è, using a semicircular protractor:
(a) subtract the given angle from 360è.
(b) construct the resulting angle (it will be less than 180è).
(c) label the required angle: it is ‘outside’ the one that has been constructed.
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5B
individual
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Activity 5-B-1
Constructing angles
doc-1740
Activity 5-B-2
More constructing
angles
doc-1741
Activity 5-B-3
Advanced
constructing angles
doc-1742
Constructing angles with a protractor
FluenCY
1 We4a Construct each of the following angles.
a 15è
b 9è
c 53è
e 45è
f 40.8è
g 88è
d 75.5è
h 76è
2 We4b Construct each of the following angles.
a 96è
b 92è
c 165.2è
e 140è
f 156.4è
g 127è
d 143è
h 149è
3 We5 Construct each of the following angles using a semicircular protractor.
a 185è
b 210.5è
c 235è
d 260è
e 243è
f 192è
g 249.8è
h 214è
4 mC To construct an angle of 212è using a semicircular protractor, we need to construct an
angle less than 180è first and then label the ‘outside’ angle. The size of the first angle to be
constructed is:
A 212è
B 58è
C 148è
D 112è
e None of these
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Interactivity
Bisectors
int-2347
5C
5 Construct each of the following angles.
a 295è
b 269è
c 307è
d 349è
e 328è
f 300è
g 345è
h 358è
reFleCtion
In what situations would a
semicircular protractor be easier
to use than a circular one?
types of angles and naming angles
types of angles
■
Angles can be classified according to their size.
An acute angle is greater than 0è,
but less than 90è.
A straight angle equals exactly
180è.
■
■
144
A right angle is an angle An obtuse angle is greater
that equals exactly 90è.
than 90è but less than 180è.
A reflex angle is greater
than 180è but less than
360è.
Angles that sum to 90è are called complementary angles.
Angles that sum to 180è are called supplementary angles.
maths Quest 7 for the australian Curriculum
A revolution or a perigon is
an angle of 360è (a full circle).
measurement anD Geometry • geometriC reasoning
WorKeD eXamPLe 6
Classify each of the following angles according to their size.
a 115è
b 27è
c 300è
tHinK
Write
a
The given angle is larger than 90è, but smaller than 180è, so
classify it accordingly.
a
115è is an obtuse angle.
b
The given angle is between 0è and 90è, so classify it accordingly.
b
27è is an acute angle.
c
The given angle is larger than 180è, but less than 360è, so
classify it accordingly.
c
300è is a reflex angle.
naming angles
■
■
■
Angles can be named using the capital letters of the English alphabet.
A common way to name an angle is to use three letters: two letters to represent the arms of
the angle, and a third letter to represent its vertex. The letter representing the vertex is always
placed in the middle (between the two letters representing the arms).
Instead of writing the word ‘angle’, we use the symbol ±.
WorKed eXamPle 7
Name each of the following angles.
a
b A
X
Y
O
B
C
tHinK
Write
a
Name the angle by starting either from X, or from Y, and
placing O (the letter for the vertex) in the middle. Remember
to place the angle symbol (±) before the letters.
a
±XOY or ±YOX
b
Name the angle by starting either from A, or from C, and
placing B (the letter representing the vertex) in the middle.
Remember to place the angle symbol (±) before the letters.
b
±ABC or ±CBA
WorKeD eXamPLe 8
Draw the acute angle ±ADG.
tHinK
1
Construct any acute angle (unless specified otherwise).
2
Letter D is in the middle, so place it at the vertex.
3
Place letter A at one arm of the angle and letter G at the
other. (Note that it does not matter which arm is represented
by AD and GD.)
DraW
A
D
G
Chapter 5
Geometry
145
measurement anD Geometry • geometriC reasoning
rememBer
1. Angles can be classified according to their size.
Name
Angle size
Diagram of angle
Acute
Between 0è and 90è
90è
Right
Between 90è
and 180è
Obtuse
Angle size
180è
Between 180è
and 360è
360è
Diagram
Name
of angle
Straight
Reflex
Revolution
2. An angle can be named using three capital letters from the English alphabet: two for
the arms and one for the vertex of the angle.
3. The letter representing the vertex of the angle is always placed in the middle. Use the
symbol ± instead of the word ‘angle’ before the three letters.
eXerCise
5C
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Activity 5-C-1
Types of angles and
naming angles
doc-1743
Activity 5-C-2
More types of angles
and naming angles
doc-1744
Activity 5-C-3
Advanced types of
angles and naming
angles
doc-1745
146
types of angles and naming angles
FluenCY
1 We6 Classify each of the following angles according to its size.
12è
b 215.3è
c 98è
d 156è
180è
f 62è
g 355.2è
h 90è
4.8è
j 360è
k 100è
l 45è
1
82è
n 270è
o 36 è
p 195è
2
2 The following list gives values of particular angles.
3è, 45è, 65è, 123è, 69è, 234è, 90è, 360è, 300è, 270è, 165è, 210è, 180è
a How many of these are acute angles? List them.
b How many of these are obtuse angles? List them.
c Is there a right angle in the list?
d Is there a straight angle?
e How many reflex angles are there? List them.
f Is there a full revolution? What is its value?
g What is the complement of 65è?
h What is the supplement of 123è?
3 Consider the diagrams below and write down the type of angle shown in each case.
a
e
i
m
a
b
c
d
e
f
maths Quest 7 for the australian Curriculum