Angles
Level D
Types of Angles
Naming Angles
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Measuring Angles
Drawing Angles
Calculating Missing angles
Vertically Opposite Angles
Compass Points
Three Figure Bearings
22-Nov-11 Created by Mr.Lafferty Math Dept
Starter Questions
Level D
Q1. Convert to the 24 hour clock.
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(a) 7:25 pm (b) 6:50 am
Q2. Is an obtuse angle less than 90 deg.
Q3. Does 234 + 47 + 2 = 313 Explain your answer?
Q4. Round the following to nearest hundred.
(a) 501 (b) 9 765
22-Nov-11 Created by Mr.Lafferty Math Dept
Type of Angles
Level D
Learning Intention Success Criteria
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1. Explain some types of 1. To be able to identify acute,
Angles at level D. right-angle, obtuse, straight line
and reflex angles.
22-Nov-11 Created by Mr.Lafferty Math Dept
Type of Angles
Level D
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Horizontal
Acute Right - Angle Obtuse
less than 90o exactly 90o Between 90o – 180o
Straight Line Angle
exactly 180o
reflex
over 180o less than 360o
22-Nov-11 Created by Mr.Lafferty Math Dept
Type of Angles
Level D
Now try
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Ch8 (page 87)
Exercise 1
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Starter Questions
Level D
Q1. Convert to the 12 hour clock.
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(a) 17:15 (b) 05:40
Q2. Write down 2 numbers that add to give 8 and
multiply to give 15.
Q3. Does 565 – 73 = 482 Explain your answer
Q4. Round the following to nearest 100.
(a) 13,551 (b) 369,449
22-Nov-11 Created by Mr.Lafferty Math Dept
Naming Angles
Level D
Learning Intention Success Criteria
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1. To explain how we name 1. To be able to name an
angles by THREE capital
letters with the angle sign. angle.
The middle letter being 2. Understand the
where the angle is. difference between the
type of angle and the
name of an angle.
22-Nov-11 Created by Mr.Lafferty Math Dept
Naming Angles
Level D
A X
D
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B C Z Y
Type of angle is right angle
Type of angle is obtuse
Name of angle is ∠ ABC
Name of angle is ∠ ZYX
Type of angle is acute
Name of angle is ∠ CBD
MIDDLE LETTER IS ALWAYS WHERE THE ANGLE IS
22-Nov-11
ALWAYS 3 CAPITAL LETTERS
Naming Angles
Level D
Now try
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Ch8 (page 88)
Exercise 2
22-Nov-11 Created by Mr.Lafferty Math Dept
Starter Questions
Level D
1. Calculate:
(a) 180 -33 (c) 52 x 7
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Q2. What is wrong with this sentence.
Convert to 24 hrs clock
(a) 23 00 hrs (b) 14 23 hrs
Q.3 What value is of x if x - 45 = 70
22-Nov-11 Created by Mr.Lafferty Math Dept
Measuring Angles
Level D
Learning Intention Success Criteria
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1. To show how to measure 1. To be able to measure
angles of various type.
angle using a protractor.
22-Nov-11 Created by Mr.Lafferty Math Dept
A 180o Protractor
Level D
Outside scale from Inside scale from
0o to 180o going in a 0o to 180o going in an
clockwise direction. anti-clockwise direction.
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You need to be able to measure an angle to the nearest
degree. To help you do this you should always:
1. Look directly down onto the cross point.
Level D
2. Always use the protractor in a horizontal manner as shown
below.
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Measuring 1
Angles with a
180o Protractor
Level D
50o
2
0 on the inside so
use inside scale
67o
0 on the outside so
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use outside scale 14
Measuring 3
Angles with a 120o
180o Protractor
Level D
4
135o 0 on the inside so
use inside scale
0 on the outside so
22-Nov-11
use outside scale 15
Measuring Angles
Level D
Now try
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Ch8 (page 90)
Exercise 3
22-Nov-11 Created by Mr.Lafferty Math Dept
Starter Questions
Level D
1. Calculate:
(a) 180 -33 (c) 52 x 7
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Q2. Convert to 12 hrs clock
(a) 23 00 hrs (b) 14 23 hrs
Q.3 What value is of x if x - 45 = 70
22-Nov-11 Created by Mr.Lafferty Math Dept
Drawing Angles
Level D
Learning Intention Success Criteria
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1. To show how to daarw 1. To be able to draw an
angles of various type. angle using a ruler and
protractor.
22-Nov-11 Created by Mr.Lafferty Math Dept
Drawing Angles
Level D
Example : Draw an angle BAC of 300
Step 1 Draw line AC=6cm
Step 2 Measure an angle of 30o
B
and put an X beside it.
X
Step 3 Draw the line
through X. Label it B.
30o
A C
Step 4 Put in the angle value
and name the angle. BAC = 30o
22-Nov-11 Created by Mr. Lafferty 19
Drawing Angles
Level D
Example : Draw an angle STU of 1100
S
Step 1 Draw line TU=6cm
X
Step 2 Measure an angle of 110o
and put an X beside it.
Step 3 Draw the line
through X. Label it S.
110o
T U
Step 4 Put in the angle value
and name the angle. STU = 110o
22-Nov-11 Created by Mr. Lafferty 20
Drawing Triangles
R
Level D
o 40o Q
30
Example : Draw to scale the triangle PQR P
with PQ = 8cm and angle RPQ = 30o and RQP = 40o
Step 1 Draw line PQ 8cm
Step 2 Measure R
Angle RPQ
from P 30o
Step 3 Measure
angle RQP
from Q 40o P Q
Step 4 Where lines cross is point R
22-Nov-11 Created by Mr. Lafferty 21
Drawing Angles
Level D
Now try
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Ch8 (page 92)
Exercise 4
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Starter Questions
Level D
1. Solve the equation x-3=18
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2. Calculate 25.4 + 32.5
3. Does x o = 15o Explain ? x
o o
75
4. Change 790cm into m
22-Nov-11 Created by Mr.Lafferty Math Dept
Find Missing Angles
Level D
Learning Intention Success Criteria
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1. To calculate missing angle
give all other angles. 1. To know 360o in a circle.
2. Find the missing angle in a
right angle, straight line
and vertical opposite
angle.
22-Nov-11 Created by Mr.Lafferty Math Dept
Find Missing Angle
Level D
55o
o 115o 65o
35
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Two angles making a
o
Two angles making a straight line add to 180
o
right angle add to 90 (Supplementary angles)
(Complementary angles)
o
120 95
o
145o
Angles round a point
o
always add up to 360
22-Nov-11 Created by Mr.Lafferty Math Dept
Find Missing Angle
Level D
Now try
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Ch8 (page 93)
Exercise 5
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Starter Questions
Level D
Q1. Find the value of x
x 16 28
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Q2. Find two numbers that multiply to give 6
and add to give 5.
Q3. Does 240 ÷ 10 = 24 Explain your answer.
Q4. I divide a cake in 6 pieces and eat 1 of them.
What fraction have I eaten.
22-Nov-11 Created by Mr.Lafferty Math Dept
Vertically Opposite Angles
Level D Vertically Opposite
Learning Intention Success Criteria
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1. To explain the property of 1. To understand the term
vertically opposite angles.
vertically opposite.
2. To be able to use property
to solve problems.
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Vertically Opposite Angles
Level D
146o
o
34
o 34
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146o
angles opposite each other
at a cross are equal.
131o 49o
38o
110o o 49o o
o 142 142
o
131
70
o
70
110o 38o
22-Nov-11 Created by Mr.Lafferty Math Dept
Vertically Opposite Angles
Level D
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Now try Exercise 6
Ch8 (page 95)
22-Nov-11 Created by Mr.Lafferty Math Dept
Starter Questions
Level D
Q1. Does 182 – 75 = 103 Explain.
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Q2. Find two numbers that multiply to give 48
and divide to give 3.
Q3. Find the missing angles 119o co
ao bo
22-Nov-11 Created by Mr.Lafferty Math Dept
Compass Points
Level D
Learning Intention Success Criteria
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1. To explain the basic 1. To understand the
points on a compass in
terms of direction and directions on a compass.
degrees.
2. To be able to use compass
points and degrees to
solve problems.
22-Nov-11 Created by Mr.Lafferty Math Dept
Compass Points
360/000o
Level D N
Half way between Half way between
North and West NW North and East
NE
270o W E 090o
SW SE
Half way between Half way between
S
South and West South and East
180o
22-Nov-11 Created by Mr. Lafferty Maths Dept.
If Lewis walks to Jamie
If Daniel is to Julie
If Laura walks facing
If Danielle is facing Paul
If Daniel is facing North
then to is South West
then toRyan and East
Frances North then
Who North of and
Danielle
and turns
Who isanti-clockwise
and turns clockwise to
and turns
Who istoto where
back of Lewis Daniel
Who is where Jamie
then back East of heshe
clockwise to face
Compass Points
of How
face Laura. Ryan many
to face Daniel. How many
Level D started. Write down all
Danielle. How many
degrees is this.
degrees is this.
the directions he took.
the directions she took.
degrees is this.
Jamie Frances Ryan
N
Julie Daniel Laura
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Lewis Danielle Paul
22-Nov-11 Created by Mr. Lafferty Maths Dept.
Compass Points
Level D
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Now try Exercise 8
Ch8 (page 98)
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Starter Questions
Level D
1. 99.6 + 7.27
2. If I am facing NW and turn 180o
clockwise. Which direction am I facing now.
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3. The difference in time between
0910 hrs and 1135 hrs is 2 hrs and 25 mins
Show how you work this out.
22-Nov-11 Created by Mr. Lafferty Maths Dept.
Bearings
Level D
Learning Intention Success Criteria
1. Understand what bearing is.
1. To explain what a bearing
is and how to measure and
2. Measure and draw a bearing.
draw a bearing.
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22-Nov-11 Created by Mr. Lafferty Maths Dept.
Bearings
360/000o
N
1. Measured from North.
Level D 060o
2. In a clockwise direction. 60o
270o W E 090o
3. Written as 3 figures.
S
180o
N N N
315o
W 145o E W E W E
230o 315o
230o
145o
S S S
A 360o Bearings Use your protractor to
protractor is measure the bearing
used to measure 360/000o of each point from the
centre of the circle.
bearings.
Level D 350o
315o
N 020o (Worksheet 1)
045o
NW
NE
290o
080o
270o W E 090o
250o 110o
SW SE
225o 210o 135o
S 160o
180o
Worksheet 1
N
360/000o
030o
330o
Estimate the
315o 045o
Level D bearing of
each aircraft
290o from the
centre of the
075o
radar screen.
W 270o 090o E
110o Air Traffic
Control 250o
Controller
Tower
135o
225o
170o
200o
180o
22-Nov-11
S
Created by Mr. Lafferty Maths Dept.
Drawing a Bearings
Level D
Draw a bearing of (a) 50o (b) 230o
N
N
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50o
230o
22-Nov-11 Created by Mr. Lafferty Maths Dept.
Compass Points
360/000o
Level D N
315o 045o
NW
NE
270o W E 090o
SW SE
225o 135o
S
Worksheet 1 180o
22-Nov-11 Created by Mr. Lafferty Maths Dept.
My True My True
Estimated Bearing Error Estimated Bearing Error
Bearing Bearing
Level D 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 11
12 12
Total Error Total Error
Average Error Average Error
Worksheet 2 (Radar)
Bearings
Level D
Now try Ex 9
Ch8 (page 100)
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22-Nov-11 Created by Mr. Lafferty Maths Dept.