Targeting Grade C

Angles

SSM1

GCSE Mathematics

Practice 1:: To recognise vertically opposite, alternate (Z), corresponding (F) and interior angles

Practice 2: To remember that angles in a triangle add up to 180º

Question 1

Practice 3: To remember that the angles in a quadrilateral add up to 360º

Practice 4:To work out sum of the interior angles of your polygon. A formula will help

Questions 2

Can you:

Use angle facts to calculate angles:

•Associated with parallel lines

•In a triangle

•Try some questions

•In a quadrilateral

•In any polygon

•Try some questions

If not you need

Angles associated with parallel lines

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These are all parallel lines.

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What is the connection between the yellow angles?

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They are equal because the are in corresponding positions. They are

called corresponding angles

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Notice that even though the size of the angles change, they are still equal.

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They are equal because the are in corresponding positions. They are

called corresponding angles

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These are vertically opposite angles.

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What do you think the relationship is between them?

These angles are called

alternate angles.

They are equal.

Click to continue

What are the yellow angles called?

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What are the blue angles called?

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What is the link between the size of the yellow angles and the blue

angles?

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These angles are called interior

angles.They are inside the parallel lines.

Click to continue

These are

also interior angles.

Click to continue

What do you think is the relationship between these?

Click to continue

136ºx

Find the missing angle marked x

95ºx

Find the missing angle marked x

125º

x

Find the missing angle marked x

105º x

zy

Find the sizes of the angles marked with letters

95º

a

c

b

Click for answers

X = 75º

Y = 105º

Z = 105º

a = 85º

b = 85º

c = 85º

Which angle do you need to work out first?

124º

x

y

Find the missing angles marked x and y

118º

x

Find the missing angle marked x

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Angles in a triangle

What are the yellow angles called?

What are the red angles called?

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Notice the red, yellow and green angles.

Click to continue

They are inside the purple triangle.

and on a straight line.

So the number of degrees in a Triangle

must be the same as in a straight line.

Click to continue

Which is?

a

60º 45º

Find angle a

b

37º

48º

Find angle b

c

40º

c

Find the angles marked c

3x

x

2xBack to objectives

What is the size of each of the angles?

Questions 1

Questions to practice angles associated with

parallel lines and in triangles

SSM 1Conundrum - Calculating angles 1

You can use what you know about angles to calculate angle and angle .There is more than one way to calculate these angles.

How many different ways are there?Explain.

Are there any other angles here that you could calculate?Explain

Calculating angles 2

Explain how you would calculate angle and angle The line AD looks as though it could be equal to the line CD. Is it?How do you know?

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Angles in a quadrilateral

Every quadrilateral can be divided into two triangles each containing 180º

2 x 180 = 360º

1

2

1

2

12

1

2

70º x

y

Find the missing angles

75ºx

y

Find the missing angles

x

60º

55º

x = º

145º

x

100º

55º x = º

95º

x

200º

25º

x = º

115º

x x

x = º

2x

2x

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Angles in a polygon

Formula to use to calculate the sum of the

interior angles in a polygon

(n – 2) x 180 = total number of degrees

n is the number of sides in the polygon

If you forget this formula you can always divide the shape into triangles

Can be divided into three triangles

Each triangle has an angle sum of 180º

So, angle sum of the pentagon is 3 x 180 = 540º

1

2

3

How many sides does the shape have?

Apply the formula (n-2) x 180 to find the sum of the interior angles

If this is a regular hexagon , calculate the size of each of the interior angles

Click for answers

6

(6 – 2) x 180

= 4 x 180

= 720º

720 ÷ 6 = 120º

x

70º 70º

x = º

140º

130º

x

110º 100º

x = º

110º

120º

x

140º

140º

x = º

140º

140º

80º

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Questions 2

Practice questions using angles associated

with quadrilaterals and polygons

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