Forming Angles
Unit for Measuring Angles
1
Let’
s h
ave
a M
ath
Ch
at
Angles
Types of Angles and Naming Angles
Measuring Angles
Drawing Angles
Forming Angles
2
How is an angle
formed?
Forming Angles
3
An angle is formed when
two straight lines meet at a point.
arm angle
arm The two lines are called the
arms.
The point where the straight lines meet is
called the vertex.
Use an arc ‘ ’ to indicate an angle.
Forming Angles
4
An angle can also be formed in
another way.
angle new
position
P
An angle is formed when
OP turns about O
from the original position
to a new position.
P
O
original
position
Forming Angles
5
Compare the sizes of this pair of
angles. Which is larger?
Forming Angles
6
Compare the sizes of another pair of
angles. Which is larger?
Sometimes we cannot compare the
sizes of angles by observations. We
need another method.
Unit for Measuring Angles
7
What is the unit for
measuring angles?
Unit for Measuring Angles
8
The unit we commonly use in
measuring the size of an angle is degree.
The symbol for degree is ‘°’.
e.g.
60°
The size of the above
angle is 60°. The size of the above
angle is 58°.
58°
Which angle is larger?
Unit for Measuring Angles
9
Now I am going to introduce round
angle, straight angle and right angle.
Unit for Measuring Angles
10
When an object rotates one turn and
comes back to its original position,
we say that the object rotates
one complete revolution.
The angle formed by one complete revolution is
called a , which has a size of . 360° round angle
Round angle
Unit for Measuring Angles
11
Half of a round angle, which has a size of ,
is called a .
180° straight angle
Straight angle
One quarter of a round angle, which has a size
of , is called a . 90° right angle
Right angle
The symbol ‘ ’ is
used to represent a
right angle.
Types of Angles and Naming Angles
12
The following table shows the types of
angles classified by their sizes.
Type of angle
Size
Example
Acute angle Right angle Obtuse angle
Greater than 0° and
less than 90° 90°
Greater than 90° and
less than 180°
Types of Angles and Naming Angles
13
The following table shows the types of
angles classified by their sizes.
Type of angle
Size
Example
Straight angle Reflex angle Round angle
180° 360° Greater than 180°
and
less than 360°
Types of Angles and Naming Angles
14
How to name an
angle?
Types of Angles and Naming Angles
15
The following shows several ways to
name an angle.
Angle
Name of angle x
X
Y Z Y x
XYZ, ZYX Y
Types of Angles and Naming Angles
16
Take a look at the following figure.
x
X
Y Z
W Since WYX, XYZ and
WYZ are angles with vertex Y, Y cannot identify a
specific angle.
x Y
Z
W
Y Z
W
Y Z
W
reflex WYZ x WYZ
The marked reflex
angle with vertex Y can
be named as x or
reflex WYZ.
Types of Angles and Naming Angles
17
In the following, Q is a point on PR. Determine
whether each of the following pairs of angles
represent the same angle. Put a tick ‘✓’ if they
do and a cross ‘✗’ if they do not.
P
R
Q
S
(a) PSQ and PQS
✗
✓
✓
✗
✗
✓
(b) Q and SQR
(c) RSQ and QSR
(d) P and RSP
(e) PRS and QRS
(f) QSR and RSQ
Angle Types of angles
A right angle A straight angle
A reflex angle An acute angle
An acute angle A round angle
Types of Angles and Naming Angles
18
In the following, circle the angle
with its corresponding type.
(a) round angles 1
2
(b) 3 right angles
(c) 2 straight angles
Types of Angles and Naming Angles
19
Express the size of each of the following angles in degrees.
Example 1
(c) 2 round angles (d) round angles 13
4
(a) straight angles 1
2(b) right angles
1
3
180° × 1
2
= 90°
90° × 1
3
= 30°
360° × 2
= 720° 360° × 13
4
= 630°
Types of Angles and Naming Angles
20
Write down the types of angles
marked in the figure.
A
B
D
C
E F
a
b
c
d
e
f
The sizes of a and e are 90°, therefore they are right angles.
The sizes of b and d are greater
than 0° and less than 90°, therefore they are acute angles.
The size of f is greater than 90° and less than 180°, therefore it
is an obtuse angle.
The size of c is greater than
180° and less than 360°, therefore it is a reflex angle.
Measuring Angles
21
How to measure
an angle?
Measuring Angles
22
We usually use a protractor to
measure the size of an angle.
Shows 0° to
180° in a
clockwise
direction
Shows 0° to 180° in an
anticlockwise
direction
On each scale, the straight angle
is divided into 180 equal parts,
each part indicates 1°.
Measuring Angles
23
The steps of measuring an angle
are as follows.
Step 1: Place the protractor on top of the
angle with the centre exactly on
the top of the vertex.
A
B
C
Measuring Angles
24
The steps of measuring an angle
are as follows.
A
B
C
Step 2: Align the base line of the protractor with
one arm of the angle.
Measuring Angles
25
The steps of measuring an angle
are as follows.
A
B
C
Step 2: Align the base line of the protractor with
one arm of the angle.
Measuring Angles
26
The steps of measuring an angle
are as follows.
A
B
C
Step 3: Read the scale carefully where the
other arm of the angle lies to obtain the
size of the angle.
∴ ABC = 30
Measuring Angles
27
e.g. Find the size of by using a protractor. ÐDEF
∴ DEF = 120
Measuring Angles
28
Find the size of each of the following
angles by using a protractor.
70° (a)
Measuring Angles
29
Find the size of each of the following
angles by using a protractor.
140°
(b)
Drawing Angles
30
How to draw
an angle?
Drawing Angles
31
We can draw an acute or obtuse angle
with the help of a protractor.
The steps of drawing an angle of 50° are as follows.
Step 1: Draw a line segment BC and
take B as the vertex of the angle.
Drawing Angles
32
Step 2: Place the protractor on the top of BC
with the centre of the protractor exactly
on the top of the point B.
Then align the base line of the
protractor with BC.
Drawing Angles
33
Step 3: Mark a point A on the scale
according to the required size.
Drawing Angles
34
Step 4: Remove the protractor. Join the point A
and the vertex B to give the required
angle. Write down ‘50’.
Drawing Angles
35
We can draw reflex angles in a similar way.
The steps of drawing an angle of 230° are as follows.
Step 1: Since 230° = 360° − 130°, we first draw an obtuse angle of 130°.
Drawing Angles
36
Step 2: Mark the reflex angle.
Remember not to mark the obtuse angle.
230
Drawing Angles
37
In each of the following,
draw the given angle.
(a) 80° (b) 115°
80° 115°