Measurement

Angles in Degrees

1

Sort the Angles (A)

Sort each angle into the correct type.

45°
90°
120°
30°
90°
150°
75°
135°
Acute (less than 90°)
Right (90°)
Obtuse (more than 90°)
2

Sort the Angles (B)

Sort each angle.

10°
90°
180°
170°
55°
100°
89°
91°
Acute
Right
Obtuse
Straight (180°)
3

Match Angles to Descriptions

Draw a line from each angle type.

Acute angle
Right angle
Obtuse angle
Straight angle
Reflex angle
exactly 180°
less than 90°
exactly 90°
between 90° and 180°
more than 180°
4

Identify the Angle Type (A)

Circle the angle type.

35° is a...

acute
right
obtuse

90° is a...

acute
right
obtuse

145° is a...

acute
right
obtuse

180° is a...

right
obtuse
straight
5

Identify the Angle Type (B)

Circle the angle type.

89° is...

acute
right
obtuse

91° is...

acute
right
obtuse

1° is...

acute
right
obtuse

179° is...

acute
right
obtuse
6

Angle Sequence

Fill in the missing angles counting by 45°.

45
135
180
?
180
270
360
?
?
7

Angle Bonds to 90°

Two angles make a right angle. Find the missing angle.

90
45
?
90
30
?
90
60
?
90
15
?
90
75
?
90
50
?
8

Angle Bonds to 180°

Two angles make a straight line. Find the missing angle.

180
90
?
180
60
?
180
120
?
180
45
?
180
135
?
180
100
?
9

Name That Angle

Write whether each angle is acute, right, obtuse, straight or reflex.

52° is ___

90° is ___

167° is ___

180° is ___

250° is ___

10

Estimate the Angle (A)

Circle the best estimate for each angle.

A corner of a book is...

45°
90°
120°

Half a right angle is...

30°
45°
60°

A straight line is...

90°
135°
180°

A quarter turn is...

45°
90°
180°
11

Estimate the Angle (B)

Circle the best estimate.

The angle between clock hands at 2 o'clock is about...

30°
60°
90°

The angle of an open laptop screen is about...

90°
120°
180°

A slice of pizza (1/8 of the whole) has an angle of...

30°
45°
60°

The angle at the tip of an equilateral triangle is...

45°
60°
90°
12

Calculate Missing Angles (A)

Angles on a straight line add up to 180°.

Two angles on a straight line: one is 60°. The other is ___°

Two angles on a straight line: one is 110°. The other is ___°

A right angle is divided into two parts. One is 35°. The other is ___°

Three angles on a straight line: 40°, 50° and ___°

13

Calculate Missing Angles (B)

Angles around a point add up to 360°.

Three angles around a point: 120°, 90° and ___°

Two angles around a point: 200° and ___°

Four angles around a point: 80°, 100°, 70° and ___°

14

Match Angles to Turns

Draw a line from each turn to its angle.

Quarter turn
Half turn
Three-quarter turn
Full turn
180°
360°
90°
270°
15

Angles in Shapes (A)

Use angle facts to find missing angles.

A triangle has angles of 60° and 80°. The third angle is ___° (angles in a triangle = 180°)

A triangle has angles of 45° and 45°. The third angle is ___°

A triangle has a right angle and a 35° angle. The third angle is ___°

16

Angles in Shapes (B)

Find the missing angles.

A rectangle has four ___° angles

A square has angles totalling ___°

An equilateral triangle has three angles of ___° each

The angles in any quadrilateral add up to ___°

17

Angle Facts True or False

Circle TRUE or FALSE.

Angles in a triangle always add up to 180°

TRUE
FALSE

A right angle is exactly 90°

TRUE
FALSE

Angles on a straight line add up to 180°

TRUE
FALSE

An equilateral triangle has three equal angles

TRUE
FALSE
18

Angle Problems (A)

Solve each problem. Show your working.

A triangle has angles of 60° and 80°. What is the third angle? What type of triangle is this?

Draw here

A clock shows 3 o'clock. What angle do the hands make? What about at 6 o'clock?

Draw here

Two angles in a triangle are both 45°. What is the third angle? What type of triangle is this?

Draw here
19

Angle Problems (B)

Solve these problems.

Two straight lines cross. One angle is 70°. Find the other three angles.

Draw here

A quadrilateral has angles of 80°, 110° and 95°. What is the fourth angle?

Draw here
20

Clock Angles

Calculate the angle between clock hands.

At 1 o'clock: ___°

At 4 o'clock: ___°

At 6 o'clock: ___°

At 9 o'clock: ___°

What pattern do you notice? Each hour = ___°

21

Design with Angles

Use angles to answer these.

A pizza is cut into 8 equal slices. What angle is each slice?

A spinner has 5 equal sections. What angle is each section?

A pie chart shows 25% for sport. What angle does the sport section have?

22

Create Angle Problems

Write your own angle problems.

Write a problem about missing angles on a straight line. Then solve it.

Draw here

Write a problem about angles in a triangle. Then solve it.

Draw here
23

Angle Bonds to 360°

Angles around a point add to 360°. Find the missing angle.

360
180
?
360
90
?
360
270
?
360
120
?
360
200
?
360
45
?
24

Angles in Quadrilaterals

Angles in a quadrilateral add up to 360°.

A quadrilateral has angles 90°, 90°, 90° and ___°

A quadrilateral has angles 80°, 100°, 70° and ___°

A parallelogram has two angles of 60°. What are the other two angles?

25

Estimate Angles in Real Life

Circle the best estimate.

Angle of an open book

30°
90°
180°

Angle of a ramp for a wheelchair

45°
90°

Angle of a roof peak

30°
90°
135°

Angle you turn when making a U-turn

90°
180°
360°
26

Angle Calculations (A)

Calculate each missing angle.

A right angle divided into 3 equal parts: each angle = ___°

A straight angle divided into 4 equal parts: each angle = ___°

A full turn divided into 8 equal parts: each angle = ___°

Two complementary angles: one is 25°, the other is ___°

27

Angle Calculations (B)

Find the missing angles.

Supplementary angles: one is 65°, the other is ___°

Vertically opposite angles: if one is 110°, the opposite angle is ___°

An isosceles triangle has a base angle of 50°. What are all three angles?

28

Sort Angles by Size

Sort these angles from smallest to largest.

45°
90°
120°
180°
15°
160°
270°
88°
Less than 90°
Exactly 90°
90° to 180°
180° or more
29

Match Angles to Fractions of a Turn

Draw a line.

90°
180°
270°
360°
45°
1/8 turn
1/4 turn
1/2 turn
3/4 turn
full turn
30

Interior Angles of Regular Shapes

Circle the interior angle.

Each angle in an equilateral triangle

45°
60°
90°

Each angle in a square

60°
90°
120°

Each angle in a regular hexagon

90°
120°
150°
31

Angle Word Problems

Solve these.

Two angles on a straight line are in the ratio 1:2. What are the two angles?

A triangle has one angle of 90°. The other two are equal. What are they?

A reflex angle and its non-reflex pair add to 360°. If the reflex angle is 250°, what is the other?

32

Compass Directions and Angles

Compass turns are measured in degrees.

North to East is a turn of ___°

North to South is a turn of ___°

North to West (clockwise) is a turn of ___°

North to North-East is a turn of ___°

33

Identify the Angle Type (C)

Circle the angle type.

15° is...

acute
right
obtuse

90° is...

acute
right
obtuse

170° is...

acute
obtuse
reflex

200° is...

obtuse
straight
reflex
34

Identify the Angle Type (D)

Circle the angle type.

360° is a...

straight angle
reflex angle
full turn

100° is...

acute
right
obtuse

270° is a...

obtuse
reflex
straight

45° is...

acute
right
obtuse
35

Name That Angle (B)

Write the angle type.

22° is ___

90° is ___

135° is ___

180° is ___

300° is ___

360° is ___

36

Sort the Angles (C)

Sort each angle.

60°
90°
110°
220°
30°
175°
350°
85°
Acute
Right
Obtuse
Reflex
37

Angle Bonds to 90° (B)

Find the missing angle to make a right angle.

90
25
?
90
40
?
90
55
?
90
10
?
90
70
?
90
35
?
38

Angle Bonds to 180° (B)

Find the missing angle to make a straight line.

180
75
?
180
110
?
180
30
?
180
145
?
180
55
?
180
90
?
39

Match Angles to Types (A)

Draw a line.

42°
90°
156°
180°
310°
Reflex
Acute
Right
Obtuse
Straight
40

Estimate the Angle (C)

Circle the best estimate.

The angle of a skateboard ramp

15°
45°
90°

The angle at the point of a kite

30°
60°
120°

Angle between hands at 5 o'clock

120°
150°
180°

The angle of a slide in a playground

30°
90°
150°
41

Calculate Missing Angles (C)

Find the missing angle.

Three angles on a straight line: 55°, 65° and ___°

Four angles around a point: 90°, 90°, 80° and ___°

Two angles on a straight line: one is three times the other. What are they?

42

Angles in Shapes (C)

Find missing angles.

A triangle has angles 40° and 70°. Third angle: ___°. What type of triangle?

A quadrilateral has angles 90°, 80° and 110°. Fourth angle: ___°

A regular pentagon: sum of angles = ___°. Each angle = ___°

43

Angle Facts (B)

Circle TRUE or FALSE.

Vertically opposite angles are equal.

TRUE
FALSE

Angles in a quadrilateral add to 180°.

TRUE
FALSE

A reflex angle is more than 180°.

TRUE
FALSE

Complementary angles add to 90°.

TRUE
FALSE
44

Clock Angles (B)

Calculate the angle.

At 2 o'clock: ___°

At 5 o'clock: ___°

At 10 o'clock: ___°

At 8 o'clock: ___° (smaller angle)

45

Match Clock Times to Angles

Draw a line.

3 o'clock
6 o'clock
12 o'clock
9 o'clock
90°
180°
0° (or 360°)
270° (or 90°)
46

Angle Problems (C)

Solve.

In a right-angled triangle, one angle is 35°. What is the third angle?

The angles of a triangle are in the ratio 1:2:3. Find all three angles.

Two lines cross making an angle of 55°. Find all four angles at the intersection.

47

Angle Reasoning

Explain your thinking.

Why can a triangle never have two obtuse angles?

Can a triangle have two right angles? Explain.

What is the maximum number of acute angles a quadrilateral can have?

48

Angle Bonds to 270°

Three right angles make 270°. Find the missing angle.

270
90
?
270
180
?
270
45
?
270
135
?
270
60
?
270
150
?
49

Interior Angles of Polygons

Use the formula (n-2) × 180° for the sum of interior angles.

Triangle (3 sides): sum = ___°

Quadrilateral (4 sides): sum = ___°

Pentagon (5 sides): sum = ___°

Hexagon (6 sides): sum = ___°. Each angle in a regular hexagon = ___°

50

Angle Problems — Mental Maths

Circle the correct answer.

Two angles on a straight line: 75° and ___°

75°
95°
105°

Three equal angles in a triangle: each is ___°

45°
60°
90°

Angles around a point: 3 equal angles, each is ___°

90°
120°
180°

A pentagon has angle sum ___°

360°
540°
720°
51

Match Angle Types to Degree Ranges

Draw a line.

0° to 90°
Exactly 90°
90° to 180°
Exactly 180°
180° to 360°
Reflex angle
Right angle
Straight angle
Obtuse angle
Acute angle
52

Sort Angles into Types

Sort each angle.

33°
90°
150°
180°
240°
78°
95°
310°
Acute
Right
Obtuse
Straight
Reflex
53

Angle Problems (D)

Find the missing angles.

Angles in a quadrilateral: 85°, 95°, 100° and ___°

Angles in a pentagon: 110°, 120°, 100°, 90° and ___°

A triangle has angles in ratio 1:2:3. What are the three angles?

54

Angles on a Grid

Use coordinate grid directions.

Moving from (0,0) directly right then directly up traces an angle of ___°

A diagonal line from (0,0) to (3,3) makes an angle of ___° with the horizontal

Two lines at 90° to each other are called ___

55

Angle Types in Architecture

Count angle types found in a building survey.

Right angles
Acute angles
Obtuse angles
Reflex angles
1

What type appeared most?

2

Total angles counted?

3

What fraction are right angles?

4

Why are right angles so common in buildings?

56

Angle Estimates

Students estimated angles in a picture. Count their answers.

ItemTallyTotal
Acute
Right
Obtuse
Reflex
57

Angle Patterns

Find patterns in angles.

Each interior angle of a regular triangle = ___°. Each interior angle of a regular hexagon = ___°. Each interior angle of a regular 12-gon = ___°.

As the number of sides increases in a regular polygon, what happens to each interior angle? ___

58

Angles in Everyday Life

Estimate angles in each situation.

The angle of a typical staircase step (rise/run): about ___°

The angle of a car's windshield: about ___°

The angle you lean when cycling around a corner: about ___°

Find 2 right angles and 2 obtuse angles in your home. Describe where they are.

59

Angle Facts (C)

Circle TRUE or FALSE.

The sum of angles in any triangle is always 180°.

TRUE
FALSE

A reflex angle is between 90° and 180°.

TRUE
FALSE

Angles in a hexagon sum to 720°.

TRUE
FALSE

All right angles are equal to 90°.

TRUE
FALSE
60

Using a Protractor

Describe how to measure an angle with a protractor.

Step 1: Place the protractor's ___ point on the vertex of the angle.

Step 2: Align the ___ line with one arm of the angle.

Step 3: Read the scale where the ___ arm crosses the curved edge.

If an angle looks obtuse but you read 40°, you should read the ___ scale instead.

61

Angle Investigation

Investigate angle sums.

Draw any quadrilateral. Measure all four angles. Sum = ___°. Is this always 360°?

Draw here

Draw any triangle. Tear off the corners. Arrange them along a straight line. What do you notice?

62

Match Angle to Degrees (B)

Draw a line.

One full turn
Three-quarter turn
Half turn
Quarter turn
One-eighth turn
45°
90°
180°
270°
360°
63

Supplementary Angle Bonds

Two supplementary angles add to 180°. Find the missing angle.

180
70
?
180
115
?
180
35
?
180
157
?
180
88
?
180
23
?
TipExtension: Supplementary and complementary angle terminology is extension content beyond the core Year 5 curriculum. Students who grasp basic angle facts are well prepared for this.
64

Angles in Triangles (B)

Find the missing angle in each triangle.

45°, 75°, ___°

90°, 35°, ___°

120°, 30°, ___°

55°, 55°, ___°

72°, 48°, ___°

65

Angles in Quadrilaterals (B)

Find the missing angle in each quadrilateral (angles sum to 360°).

90°, 90°, 80°, ___°

100°, 110°, 70°, ___°

120°, 120°, 60°, ___°

95°, 85°, 105°, ___°

66

Sort Angles (D)

Sort each into the correct range.

30°
60°
120°
200°
45°
89°
90°
350°
0°-45°
45°-90°
90°-180°
180°-360°
67

Angle Types in Polygons

Circle the correct answer.

A regular hexagon has interior angles of ___°.

90°
108°
120°

A regular pentagon has interior angles of ___°.

100°
108°
120°

A regular octagon has interior angles of ___°.

120°
135°
150°

A regular decagon (10 sides) has interior angles of ___°.

144°
162°
168°
68

Angles and Bearings Introduction

Bearings are measured clockwise from North.

North = 000°. East = ___°. South = ___°. West = ___°.

North-East = ___°. South-East = ___°. South-West = ___°.

A ship sails on a bearing of 090°. Which direction is it going? ___

69

Measuring Angles Practice

Estimate the following angles.

A door opened to about 1/4 open: ___°

A door opened flat against a wall: ___°

The minute hand from 12 to 3 on a clock: ___°

An equilateral triangle corner: ___°

70

Angles Measured in Architecture

Students measured angles in a school building.

90° (right)
45° (acute)
135° (obtuse)
Other
1

Most common angle?

2

Total angles measured?

3

What fraction are right angles?

4

Why do buildings use mostly right angles?

71

Angle Estimation Accuracy

Students estimated an angle of 60°. Count how close they were.

ItemTallyTotal
Within 5°
5-10° off
10-20° off
More than 20° off
72

Angle Problems (E)

Solve these harder problems.

A clock shows 2:30. What angle do the hands make (consider the minute and hour hand positions)?

A gear rotates 40° each second. How many full rotations in one minute?

If you draw a diagonal in a square, it divides each corner angle into two equal angles. What is each small angle?

73

Design With Angles

Use angle knowledge to design shapes.

Design a logo using only right angles. Describe it.

Draw here

Design a pattern using only 60° angles. Describe it.

Draw here
74

Compare Angle Sizes

Which angle is larger?

75° or 60°?

vs

135° or 150°?

vs

90° or 89°?

vs
75

Match Angle Name to Size Range

Draw a line.

Acute angle
Right angle
Obtuse angle
Straight angle
Reflex angle
180°
Between 90° and 180°
Between 180° and 360°
Exactly 90°
Between 0° and 90°
76

Co-interior Angle Bonds

Co-interior angles (same side of a transversal) add to 180°.

180
60
?
180
115
?
180
73
?
180
45
?
180
130
?
180
88
?
77

Angles in Polygons (B)

Circle the correct answer.

Sum of interior angles of a triangle?

90°
180°
360°

Sum of interior angles of a quadrilateral?

180°
270°
360°

Each angle of a regular hexagon?

108°
120°
135°

Sum of exterior angles of any convex polygon?

180°
270°
360°
78

Sort Angles: Acute, Right, Obtuse, or Reflex?

Sort each angle measurement.

72°
90°
135°
210°
45°
300°
Acute (< 90°)
Right (= 90°)
Obtuse (90°–180°)
Reflex (> 180°)
79

Finding Unknown Angles (C)

Find the missing angles using angle rules.

Angles on a straight line: 35° + 75° + n° = 180°. n = ___

Vertically opposite angles: if one angle is 64°, the opposite angle is ___

A triangle has angles 48° and 65°. Third angle: ___

A quadrilateral has angles 90°, 85°, and 110°. Fourth angle: ___

80

Angles in Navigation

Compass bearings use angles.

North is 0°, East is 90°. What is South? ___ West? ___

A ship turns from North to 135°. What direction is this (between which compass points)? ___

Turn 270° clockwise from North. Where are you now? ___

81

Angle Sequences

Continue each angle sequence.

60
120
180
?
?
180
150
120
90
?
?
90
80
70
60
?
?
82

Compare Angle Types

Tick which angle is larger.

75° (acute) vs 115° (obtuse)

vs

135° (obtuse) vs 200° (reflex)

vs
83

Clock Angles (B)

Calculate angles made by clock hands.

At 3:00, the angle between the hands is ___°

At 6:00, the angle between the hands is ___°

At 12:00, the angle between the hands is ___°

At 2:00, the angle between the hands is ___°

84

Angles Found in Nature

A student measured angles found in nature.

Leaf veins (acute)
Crystal structures (90°)
Flower petal angles (72°)
Branch angles (obtuse)
1

Most common type of angle in nature?

2

Total angles measured?

3

Flower petals: 5 petals × 72° = total around centre?

4

What angle type do branch angles fall into?

85

Angles in Sport

Angles are important in sport.

A basketball free throw at 45° gives the best arc. What type of angle is 45°? ___

A skiing slalom course has gates. At a 30° angle the skier must turn. At 90° at the bottom. What is the turn type? ___

Describe one other sport where angles are important:

86

Angle Names and Properties (B)

Match each angle name to its size range.

Acute
Right
Obtuse
Straight
Reflex
180°
between 180° and 360°
exactly 90°
between 90° and 180°
between 0° and 90°
87

Angles in a Triangle (B)

Find the missing angle.

180
70
?
180
95
?
180
45
?
180
110
?
88

Angle Types in Polygons

Circle the correct answer.

All angles in a square are...

acute
right angles

A regular hexagon's interior angles are each...

120°
60°

The sum of angles in a quadrilateral is...

180°
360°

A regular triangle's angles are each...

60°
90°
89

Sort by Angle Size

Sort from smallest to largest angle.

35°
91°
270°
90°
179°
45°
200°
180°
Smallest
Largest
90

Angles Around a Point

Angles around a point sum to 360°.

Three angles meet at a point: 120°, 95°, and n°. Find n: ___

Four equal angles meet at a point. Each angle: ___

Draw a diagram showing 4 angles around a point that sum to 360°:

Draw here
91

Using a Protractor (B)

Describe how to measure angles accurately.

List the 4 steps for measuring an angle with a protractor:

A student measured 55° but the actual angle was 125°. What mistake did they make? ___

92

Angle Patterns (B)

Continue each angle sequence.

15
30
45
60
?
?
360
300
240
180
?
?
10
20
40
80
?
?
93

Angles in Architecture (B)

Architects use angles when designing buildings.

A roof makes a 35° angle with the ceiling. What is the angle on the other side (supplementary)? ___

A staircase rises at 40° to the floor. What is the angle between the staircase and the wall? ___

Why are right angles (90°) so common in buildings?

94

Compare Angle Measures (B)

Which angle is larger?

80° vs 100° — which is larger?

vs

45° vs 135° — which is larger?

vs
95

Angle Types in a Building

Count angle types found in a floor plan.

ItemTallyTotal
Right angles (90°)
Acute angles (<90°)
Obtuse angles (>90°)
Straight lines (180°)
96

Home Activity: Angle Scavenger Hunt

Find angles all around you!

  • 1Find 3 right angles in your home (corners of doors, books, tiles).
  • 2Open a door to different angles. Estimate the angle.
  • 3Look at the hands on an analogue clock at different times. Estimate the angle.
  • 4Fold a piece of paper to make angles of 45°, 90° and 180°.