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Classifiying, measuring and constructing angles

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Grade 8

INTEGERS, EQUASIONS AND GEOMETRY

Module 9

CLASSIFYING , MEASURING AND CONSTRUCTING ANGLES

1. How do you construct (draw) any size of angle?

To do this, you require the following:

compasses, protractor and ruler

General: construction of e.g. ABˆCABˆC size 12{A { hat {B}}C} {} = 60°

  1. a) Start by drawing a line

b) Make a mark on the line

c) Place your protractor’s mark in the middle of your mark

d) Read from the 0º on the right-hand side to the desired degree

Figure 1
Figure 1 (Picture 119.png)

e) Name your angle correctly [e.g. ABˆCABˆC size 12{A { hat {B}}C} {} = 60° or Bˆ1Bˆ1 size 12{ { hat {B}} rSub { size 8{1} } } {} = 60° ]

2. How would you go about constructing an angle of, for example, 330º if the protractor can measure only angle sizes up to 180º?Write down your plan below:

3. Construct the following angles and classify each and indicate the limits of degrees. E.g. 60° -- acute angle(classification) --- 0° < x < 90° (limits of°)Limits of ° are read as follows: x greater than 0° and smaller than 90°

Table 1
  Angle Sketch Classification(kind of angle) Limits of °
3.1 PQˆRPQˆR size 12{P { hat {Q}}R} {} = 75°      
3.2 ABˆCABˆC size 12{A { hat {B}}C} {} = 125°      
3.3 HFˆGHFˆG size 12{H { hat {F}}G} {} = 325°      
3.4 CDˆECDˆE size 12{C { hat {D}}E} {} = 180°      
3.5 KLˆMKLˆM size 12{K { hat {L}}M} {} = 90°      
3.6 RSˆTRSˆT size 12{R { hat {S}}T} {} = 360°      

HOMEWORK ASSIGNMENT 1

  1. There are angles all around you....Determine the size of each of the angles indicated (with the aid of your protractor),write down the size of the angle concernedand classify it.

Figure 2
Figure 2 (graphics1.png)
1.1

Figure 3
Figure 3 (graphics2.png)
1.2

1.3

Figure 4
Figure 4 (graphics3.png)

1.4

Figure 5
Figure 5 (graphics4.png)

1.5

Figure 6
Figure 6 (graphics5.png)

1.6

Figure 7
Figure 7 (graphics6.png)

1.7

Figure 8
Figure 8 (graphics7.png)

1.8

Figure 9
Figure 9 (graphics9.png)
1.9

Figure 10
Figure 10 (graphics10.png)
1.10

1.11

Figure 11
Figure 11 (graphics11.png)

1.12

Figure 12
Figure 12 (graphics12.png)

1.13

Figure 13
Figure 13 (graphics13.png)

1.14

Figure 14
Figure 14 (graphics14.png)

1.15

1.16

Figure 15
Figure 15 (graphics16.png)

2. Construct the following angles by using your ruler and protractor.

2.1 A watch with an angle of 45º between the two numbers.

2.2 A sun bed with an angle of 160°

2.3 A helicopter dropping at an angle of 35º with horizontal.

2.4 A reading lamp with angles 115º and 65º.

Memorandum

CLASSWORK ASSIGNMENT 1

2. 3600 – 3300 = 300

size 12{ and } {} Construct 300

  • size 12{ and } {}Acute angle 00∠∠ size 12{∠} {}Q∠∠ size 12{∠} {} 900
  • size 12{ and } {}Obtuse angle 900∠∠ size 12{∠} {}B∠∠ size 12{∠} {} 1800
  • size 12{ and } {}Reflexangle 1800∠∠ size 12{∠} {}F∠∠ size 12{∠} {} 3600
  • size 12{ and } {}Straight (flat) angle D = 1800
  • size 12{ and } {}Right angle L = 900
  • Angle of rotation S = 3600

HOMEWORK ASSIGNMENT 1 AND 2

  • Acute ∠∠ size 12{∠} {}
  • Obtuse ∠∠ size 12{∠} {}
  • Obtuse ∠∠ size 12{∠} {}

1.4 Reflex ∠∠ size 12{∠} {}

  • Obtuse ∠∠ size 12{∠} {}
  • Acute ∠∠ size 12{∠} {}
  • Acute ∠∠ size 12{∠} {}
  • Acute ∠∠ size 12{∠} {}
  • Acute ∠∠ size 12{∠} {}
  • Acute ∠∠ size 12{∠} {}
  • Acute ∠∠ size 12{∠} {}
  • Reflex ∠∠ size 12{∠} {}
  • Acute ∠∠ size 12{∠} {}
  • Obtuse ∠∠ size 12{∠} {}
  • Obtuse ∠∠ size 12{∠} {} and Acute ∠∠ size 12{∠} {}
  • Obtuse ∠∠ size 12{∠} {} and Acute ∠∠ size 12{∠} {}

CLASSWORK ASSIGNMENT 2

1.a) Acute angle

b) one right angle

c) one obtuse angle

  • acute-angled
  • right-angled / acute-angled
  • obtuse-angled
  • right-angled

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