Angles

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Angles
National 4 REL 1.2c
Revising Basic Angles
Naming Angles
Measuring Angles
Finding Missing angles
Drawing Triangles
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Angles in a Triangle
Corresponding Angles
Alternate Angles
Angles in a Quadrilateral
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Starter Questions
National 4 REL 1.2c
Q1. Convert to the 24 hour clock.
(b) 650 am
(a) 725 pm
Q2. Write down the type of angle that is less
than 90 deg.
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Q3. Calculate 2.34 4.7 0.12
Q4. Round the following to nearest 1000.
(a) 12,501
(b) 369,765
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Type of Angles
National 4 REL 1.2c
Learning Intention
Success Criteria

1. To be able to identify acute, right-angle,
   obtuse, straight line and reflex angles.

1. To revise Type of Angles.

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Type of Angles
National 4 REL 1.2c
Acute less than 90o
Obtuse Between 90o 180o
Right Angle exactly 90o
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Straight Line Angle exactly 180o
reflex over 180o less than 360o
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Type of Angles
National 4 REL 1.2c
Now try Ch2 (page 14) Exercise 1
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Starter Questions
National 4 REL 1.2c
Q1. Convert to the 12 hour clock.
(b) 0540
(a) 1715
Q2. Write down 2 numbers that add to give 8
and multiply to give 15.
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Q3. Calculate 5.65 1.3
Q4. Round the following to nearest 100.
(a) 13,551
(b) 369,449
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Naming Angles
National 4 REL 1.2c
Learning Intention
Success Criteria

1. To be able to name an angle.

1. To explain how we name angles by THREE capital
   letters with the angle sign. The middle letter
   being where the angle is.

1. Understand the difference between the type of
   angle and the name of an angle.

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Naming Angles
National 4 REL 1.2c
A
X
Y
B
C
Z
Type of angle is acute
Type of angle is obtuse
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Name of angle is ? ABC
Name of angle is ? ZYX
MIDDLE LETTER IS ALWAYS WHERE THE ANGLE IS
ALWAYS 3 CAPITAL LETTERS
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Naming Angles
National 4 REL 1.2c
Now try Ch2 (page 15) Exercise 2
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Starter Questions
Q1. Convert to the 12 hour clock.
(b) 0540
(a) 1715
Q2. Write down lowest common multiple of 3, 4 , 5.
Q3. List the prime numbers between 10 and 20.
Q4. Round the following to nearest 100.
(a) 13,551
(b) 369,449
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A 180o Protractor
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1. Look directly down onto the cross point.
2. Always use the protractor in a horizontal
manner as shown below.
?
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Measuring Angles with a 180o Protractor
50o
67o
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Measuring Angles with a 180o Protractor
120o
135o
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Naming Angles
National 4 REL 1.2c
Now try Ch2 (page 17) Exercise 3
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Starter Questions
National 4 REL 1.2c
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Find Missing Angles
National 4 REL 1.2c
Learning Intention
Success Criteria

1. To know 360o in a circle.

1. To calculate missing angle give all other angles.

1. Find missing angle given all other angles.

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Find Missing Angle
National 4 REL 1.2c
55o
115o
Two angles making a straight line add up to
180o (Supplementary angles)
Two angles making a right angle add up to
90o (Complementary angles)
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146o
145o
146o
Angles round a point always add up to 360o
Angles opposite each other at a cross are equal.
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Angles and Triangles
National 4 REL 1.2c
1
2
y
Angle x 180 47 133o
114o
Angle y 180 114 66o
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3
4
Angle a 180 76 104o
82o
b
a
Angle b 180 82 98o
76o
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Angles and Triangles
National 4 REL 1.2c
Example Find angle x.
360o
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Angle xo 360o - (90o 100o 105o)
360o 295o 65o
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Find Missing Angle
National 4 REL 1.2c
Now try Ch2 (page 20) Exercise 4
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(SAS) Starter Questions
Q1. Convert the percentages to fractions.
(a) 30
(b) 60
Q2. Write down all the factors of 16.
Q4. Round the following to 1 decimal place.
(a) 4.549
(b) 6.551
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Drawing SAS Triangles
SAS Triangles
Side
Side
Angle
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Drawing SAS Triangles
Toolkit required
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Drawing SAS Triangles
C
30o
B
Example Draw to scale the triangle ABC with
AB 6cm and angle CAB 30o and AC 5cm
A
Step 1 Draw line AB6cm
Step 2 Measure angle CAB from A
C
X
Step 3 Draw the line AC 5cm through X. Label
it C.
A
B
Step 4 Join C to B.
Check angles add to 180o
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Find Missing Angle
National 4 REL 1.2c
Now try Ch2 (page 22) Exercise 5
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Starter Questions
National 4 REL 1.2c
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Sum of Angles in a Triangle
National 4 REL 1.2c
Learning Intention
Success Criteria

1. To know all angles in a triangle add to 180o.

• To show that all the angles
• in a triangle sum to 180o.

1. Use knowledge to solve problems.

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To determine the angle sum of any Triangle
National 4 REL 1.2c
Cut off corners ?
Cut off corners ?
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Cut off corners ?
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angle sum of any Triangle
National REL 1.2c
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180o
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Angles and Triangles
National 4 REL 1.2c
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Equilateral Triangle
Isosceles triangle
Right-angled triangle
3 equal sides 3 equal angles.
2 equal sides 2 equal angles (base)
One angle is 90o
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Angles and Triangles
National 4 REL 1.2c
Angle a 180 (90 65) 180 155
25o
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Since the triangle is equilateral, angles a, b
and c are all 60o (180/3)
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Angles and Triangles
National 4 REL 1.2c
Angle a 65o (base angles of an isosceles
triangle are equal).
b
Angle b 180 (65 65) 180
130 50o
a
65o
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Angles and Triangles
National 4 REL 1.2c
a
b
Isosceles triangle
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Sum of Angles in a Triangle
National 4 REL 1.2c
Copy out the following triangles and find the
missing angles.
xo
87o
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xo
32o
xo
xo
Remember all the angles add up to 180o
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Sum of Angles in a Triangle
National 4 REL 1.2c
Now try Ex 6 Ch2 (page 23)
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Starter Questions
National 4 REL 1.2c
Q1. Solve the equation below
Q2. Find two numbers that multiply to give
18 and subtract to give 3.
Q3. Find the average and range of the numbers
below
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2,8,8,10
Q4. Find
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Angles
Corresponding Angles
National 4 REL 1.2c
Learning Intention
Success Criteria

1. To understand the term corresponding angles.

1. To explain the term corresponding angles
and show how we use the property to solve
problems.
2. To be able to use property to solve problems.
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Angles
Corresponding Angles
National 4 REL 1.2c
Which angles are equal?
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Angles
Corresponding Angles
National 4 REL 1.2c
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Which angles are equal?
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Angles
Corresponding Angles
National 4 REL 1.2c
Which angles are equal to the shaded angle?
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Angles
National 4 REL 1.2c
Which angles are equal to the shaded angle?
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Angles
Corresponding Angles
National 4 REL 1.2c
look for
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shapes
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Angles
Corresponding Angles
National 4 REL 1.2c
What is the value of letter x?
120
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x
120
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Angles
Corresponding Angles
National 4 REL 1.2c
100
What is the value of letter a?
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a
100
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Angles
Corresponding Angles
National 4 REL 1.2c
b
48
48
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What is the value of letter b?
47
Angles
Corresponding Angles
National 4 REL 1.2c
What is the value of letter c?
110
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c
110
48
Angles
Corresponding Angles
National 4 REL 1.2c
70
What are the values of letters a and b?
b
110
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a
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Angles
Corresponding Angles
National 4 REL 1.2c
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What are the values of the missing angles?
115
50
Angles
Corresponding Angles
National 4 REL 1.2c
123
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What are the values of the missing angles?
123
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Angles
Corresponding Angles
National 4 REL 1.2c
Now try Ch2 Extension Booklet Ex7E Page 1 Q1 to
Q4
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Starter Questions
National 4 REL 1.2c
Q1. Solve the equation below
Q2. Find two numbers that multiply to give
48 and divide to give 3.
119o
Q3. Find missing angles
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bo
ao
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Angles
Alternate Angles
National 4 REL 1.2c
Learning Intention
Success Criteria

1. To understand the term alternate angles.

1. To explain the term alternate angles and
show how we use the property to solve problems.
2. To be able to use property to solve problems.
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Angles
Alternate Angles
National 4 REL 1.2c
Look for
- Z shapes
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equal angles
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Angles
Alternate Angles
National 4 REL 1.2c
Find the value of a ?
35
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a
35
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Angles
Alternate Angles
National 4 REL 1.2c
b
43
Find the value of b ?
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43
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Angles
Alternate Angles
National 4 REL 1.2c
Find the value of c ?
33
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33
c
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Angles
Alternate Angles
National 4 REL 1.2c
123
Find the value of d ?
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d
123
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Angles
Alternate Angles
National 4 REL 1.2c
50
Find the value a and b ?
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a
b
130
50
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Angles
Alternate Angles
National 4 REL 1.2c
Find the value of a and b ?
135
c
45
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45
d
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Angles
Alternate Angles
National 4 REL 1.2c
60
c
120
Find the value a, b and c ?
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b
60
120
a
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Angles
Alternate Angles
National 4 REL 1.2c
Now try Ch2 Extension Booklet Ex7E Page 4 Q5 to
Q7
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Starter Questions
National 4 REL 1.2c
Q1. List 4 properties of a square.
Q2. Simplify the following fraction
Q3. Express the following percentages as fractions
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Q4. Solve
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Angles in a Quadrilateral
National 4 REL 1.2c
IMPORTANT The angles in a quadrilateral ALWAYS
add up to 360o
B
C
bo
We have split the quadrilateral into two
triangles
co
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do
ao
But for any triangle the sum of the angles is
1800
A
D
Hence for the quadrilateral we have 2 x 180o360o
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Angles in a Quadrilateral
National 4 REL 1.2c
Question Find the missing angle below.
The four angles of a quadrilateral add to 360o
w
x
34o
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100o
yo
z
y
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Angles
Angles in a Quadrilateral
National 4 REL 1.2c
Now try Ch2 Extension Booklet Ex8E Page 7
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