4-Aug-15Created by Mr.Lafferty Math Dept Revising Basic Angles Naming Angles Finding Missing angles Angles in a Triangle Corresponding

Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept

Revising Basic Angles

Naming Angles

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Finding Missing angles

Angles in a Triangle

Corresponding Angles

Alternate Angles

AnglesAnglesNational 4 REL 1.2c

Angles in a Quadrilateral

Drawing Triangles

Measuring Angles


Starter QuestionsStarter Questions

Q3. Calculate 2.34 + 4.7 + 0.12

Q1. Convert to the 24 hour clock. (a) 7:25 pm (b) 6:50 am

Q2. Write down the type of angle that is less than 90 deg.

Q4. Round the following to nearest 1000.

(a) 12,501 (b) 369,765

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National 4 REL 1.2c


Learning IntentionLearning Intention Success CriteriaSuccess Criteria

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

1. To revise Type of Angles.

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Type of AnglesType of AnglesNational 4 REL 1.2c


Acute less than 90o

Obtuse Between 90o – 180o

Right Angle exactly 90o

reflex over 180o less than 360o

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Straight Line Angle exactly 180o

Type of AnglesType of Angles

HorizontalV

ertica

l

National 4 REL 1.2c


Now try Ch2 (page 14)

Exercise 1

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Type of AnglesType of AnglesNational 4 REL 1.2c


Starter QuestionsStarter Questionsw

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Q3. Calculate 5.65 – 1.3

Q1. Convert to the 12 hour clock. (a) 17:15 (b) 05:40

Q2. Write down 2 numbers that add to give 8 andmultiply to give 15.


(a) 13,551 (b) 369,449

National 4 REL 1.2c



1.1. To be able to name an To be able to name an angle.angle.

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

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

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Naming AnglesNaming AnglesNational 4 REL 1.2c


Naming AnglesNaming Anglesw

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A

B C

Type of angle is acute

Name of angle is ∠ ABC

Type of angle is obtuse

Name of angle is ∠ ZYX

X

YZ

MIDDLE LETTER IS ALWAYS WHERE THE ANGLE IS

ALWAYS 3 CAPITAL LETTERS

National 4 REL 1.2c



Exercise 2

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19 Apr 202319 Apr 2023 Created by Mr. Lafferty Created by Mr. Lafferty 1010

Starter QuestionsStarter Questions

Q3. List the prime numbers between 10 and 20.

Q1. Convert to the 12 hour clock. (a) 17:15 (b) 05:40

Q2. Write down lowest common multiple of 3, 4 , 5.


(a) 13,551 (b) 369,449

19 Apr 2023 11

A 180o Protractor

Outside scale from 0o to 180o going in a clockwise direction.

Inside scale from 0o to 180o going in an

anti-clockwise direction.

19 Apr 2023 12

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.

2. Always use the protractor in a horizontal manner as shown below.

19 Apr 2023 13

1

2

Measuring Angles with a

180o Protractor

0 on the outside so use outside

scale

0 on the inside so use inside scale

67o

50o

19 Apr 2023 14

3

4

Measuring Angles with a

180o Protractor

0 on the outside so use outside

scale

0 on the inside so use inside scale

135o

120o



Exercise 3

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Starter Starter QuestionsQuestions

(a) - 6 - 7 (b) -10 + (-3) (c) - 2 - 12

Q2. Convert to 12 hrs clock

(a) 23 00 hrs (b) 14 23 hrs

Q.3 Solve 5x - 45=70

1. Calculate:

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National 4 REL 1.2c



1.1. To know 360To know 360oo in a circle. in a circle.1. To calculate missing angle give all other angles. 2.2. Find missing angle Find missing angle

given all other angles.given all other angles.

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Find Missing AnglesFind Missing AnglesNational 4 REL 1.2c


120o 95

o

Find Missing Find Missing AngleAngle

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Angles round a pointalways add up to 360

o

65o

Two angles making astraight line add up to 180

o

(Supplementary angles)

Angles opposite each otherat a cross are equal.

34o 34

o

115o

146o

146o 145o

35o

Two angles making aright angle add up to 90

o

(Complementary angles)

55o

National 4 REL 1.2c

Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr Lafferty Created by Mr Lafferty 1919

x 47o

1

114o

y

2

3 4

76o

a82o

b

Angle x = 180 – 47 = 133

o

Angle y = 180 – 114 = 66o

Angle a = 180 – 76 = 104o

Angle b = 180 – 82 = 98ow

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Angles and Angles and TrianglesTriangles

National 4 REL 1.2c


Angle xo = 360

o - (90

o + 100

o +

105o)

90100105+295

Example

Find angle x.360o

105o

100ox

oThink !

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Angles and TrianglesAngles and Triangles

= 360o – 295

o = 65

o

National 4 REL 1.2c



Exercise 4

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National 4 REL 1.2c


(SAS) Starter Questions(SAS) Starter Questions

Q3. Calculate the missing angles.80

o

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


Drawing SAS TrianglesDrawing SAS Triangles

SAS TrianglesSAS Triangles

AngleAngle SideSideSideSide



Toolkit required

1.1.RulerRuler

2.2.ProtractorProtractor

3.3.Pencil & PaperPencil & Paper



Example : Draw to scale the triangle ABC with AB = 6cm and angle CAB = 30o and AC = 5cm

Step 1 Draw line AB=6cm

A B

CStep 2 Measure

angle CAB from A

Step 3 Draw the line AC = 5cm

through X. Label it C.

Step 4 Join C to B.

Check angles add to 180o

A B

C

30o

X



Exercise 5

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National 4 REL 1.2c



1. Solve the equation 5x- 3=18 (decimal value)

2. Calculate (- 13)+(- 1)- 15

3. Calculate x:

4. Change 790cm into m

5. What is the coordinate C(- 8,- 4) reflected in the x- axis?

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75o

xo

National 4 REL 1.2c


Sum of Angles in a Sum of Angles in a TriangleTriangle


1.1. To know all angles in a To know all angles in a triangle add to 180triangle add to 180oo

..1. To show that all the

angles in a triangle sum to 180

o.

2.2. Use knowledge to solve Use knowledge to solve problems.problems.

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National 4 REL 1.2c


To determine the

angle sum of any Triangle

Cut off corners

Cut off corners

Cut off corners

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National 4 REL 1.2c

Apr 19, 2023 Created by Mr.Lafferty Math Dept

angle sum of any Triangle

All angles in a triangle ALWAYS

added up to180o

180o

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National REL 1.2c


Equilateral Triangle Isosceles triangle Right-angled triangle

Angles and TrianglesAngles and Trianglesw

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3 equal sides

3 equal angles.

2 equal sides

2 equal angles (base)

One angle is 90o

National 4 REL 1.2c


Example 1

a

65o

Calculate angle a.

Angle a = 180 – (90 + 65)

= 180 – 155 = 25oExample

2Calculate angles a, b and

ca

b

cSince the triangle is equilateral,

angles a, b and c are all 60o

(180/3)


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National 4 REL 1.2c


Angle a = 65o (base angles of an isosceles triangle are equal).

a65o

Example 3Calculate angle a.

b

Angle b = 180 –(65 + 65)

= 180 – 130 = 50o

Example 4Calculate angles x and y

y

130o

x

180 - 130Angles x and y =

2o50

= =252


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National 4 REL 1.2c


180 - 90Angles a and b =

2

Example 5Calculate angles a and

b.b

a

o90 = =45

2


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Isosceles triangle

National 4 REL 1.2c



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32o

50o

38o

87o

xo

xo x

o

xo

Remember all the angles add up to 180o

National 4 REL 1.2c


Now try Ex 6 Ch2 (page 23)

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National 4 REL 1.2c



2 16 28 xQ1. Solve the equation below

Q2. Find two numbers that multiply to give 18and subtract to give 3.

Q3. Find the average and range of the numbers below

Q4. Find2,8,8,10

60% of £ 240

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National 4 REL 1.2c

Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Deptww

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1.1. To understand the term To understand the term corresponding angles.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.

AnglesAnglesCorresponding AnglesNational 4

REL 1.2c


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AnglesAnglesCorresponding Angles

Which angles are equal?

National 4 REL 1.2c


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Which angles are equal?

National 4 REL 1.2c


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Which angles are equal to the shaded angle?

National 4 REL 1.2c


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AnglesAngles

Which angles are equal to

the shaded angle?

National 4 REL 1.2c


look for

shapes

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REL 1.2c


120

x120

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AnglesAngles

What is the value of letter x?

Corresponding AnglesNational 4 REL 1.2c


100

a100

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AnglesAngles

What is the value of letter a?



48

b48

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AnglesAngles

What is the value of letter b?



110

c110

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AnglesAngles

What is the value of letter c?



70

a

70

b110

What are the values of letters a and b?

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REL 1.2c


115

65115 65 What are the values of

the missing angles?

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REL 1.2c


57

123

57

123

What are the values of the missing

angles?

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REL 1.2c


Now try Ch2 Extension Booklet

Ex7E Page 1 Q1 to Q4

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REL 1.2c



4 7 9 x

Q1. Solve the equation below

Q2. Find two numbers that multiply to give 48and divide to give 3.

Q3. Find missing angles119o

ao

bo

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National 4 REL 1.2c


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1.1. To understand the term To understand the term alternate angles.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.

AnglesAnglesAlternate AnglesNational 4

REL 1.2c


Look for

- Z shapes

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AnglesAnglesAlternate Angles

= equal angles

National 4 REL 1.2c


35

a35

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Find the value of a ?

National 4 REL 1.2c


b

43

43

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Find the value of b ?

National 4 REL 1.2c


33

33c

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Find the value of c ?

National 4 REL 1.2c


123

d123

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Find the value of d ?

National 4 REL 1.2c


50

ab130 50

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Find the value a and b ?

National 4 REL 1.2c


135

c45

d

45

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Find the value of a and b ?

National 4 REL 1.2c


60

ab

c120

60120

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Find the value a, b and c ?

National 4 REL 1.2c



Ex7E Page 4 Q5 to Q7

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AnglesAnglesAlternate AnglesNational 4

REL 1.2c

Wednesday 19 April 2023Wednesday 19 April 2023 6363Created by Mr.LaffertyCreated by Mr.Lafferty

Q3. Express the following percentages as fractions


35100

2 4 22x

Q1. List 4 properties of a square.

Q2. Simplify the following fraction

Q4. Solve

( ) 25% (b) 12.5%a

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National 4 REL 1.2c

Wednesday 19 April 2023Wednesday 19 April 2023


and ABC ACD

IMPORTANT : The angles in a quadrilateral ALWAYS add up to 360o

C

DA

B

We have split the quadrilateral into two triangles

But for any triangle the sum of the angles is 180

0

Hence for the quadrilateral we have 2 x 180o=360

o

ao

cob

o

do

360o o o o oa b c d

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National 4 REL 1.2c

Wednesday 19 April 2023Wednesday 19 April 2023 6565Created by Mr.LaffertyCreated by Mr.Lafferty


90 34 100 360o o o o oy

360 224o o oy

Question : Find the missing angle below.

x

yz

w34

o

100o

The four angles of a quadrilateral add to = 360o

136o oyy

o

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National 4 REL 1.2c



Ex8E Page 7

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AnglesAngles in a QuadrilateralNational 4

REL 1.2c

Documents

4-Aug-15Created by Mr.Lafferty Math Dept Revising Basic Angles Naming Angles Finding Missing angles Angles in a Triangle Corresponding