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Forming Angles

Unit for Measuring Angles

1

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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.


7

What is the 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?


9

Now I am going to introduce round

angle, straight angle and right angle.


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


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.


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°


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°


14

How to name an

angle?


15

The following shows several ways to

name an angle.

Angle

Name of angle x

X

Y Z Y x

XYZ, ZYX Y


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.


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


18

In the following, circle the angle

with its corresponding type.

(a) round angles 1

2

(b) 3 right angles

(c) 2 straight 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°


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


are as follows.

A

B

C

Step 2: Align the base line of the protractor with

one arm of the angle.

Measuring Angles

25


are as follows.

A

B

C

Step 2: Align the base line of the protractor with

one arm of the angle.

Measuring Angles

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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

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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

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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°

angles - tcss.edu.hk · forming angles 3 an angle is formed when two straight lines meet at a...

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