Chapter 4 of 8

All 8 chapters
  1. 1Straight lines and parallel lines, readunderstood
  2. 2Polygons, readunderstood
  3. 3Right angles and turns, readunderstood
  4. 4Measuring angles in degrees, readunderstood
  5. 5Triangles and four sided shapes, readunderstood
  6. 6Lines of symmetry, readunderstood
  7. 7Solid shapes and nets, readunderstood
  8. 8Grids and directions, readunderstood

M2.5.4 Chapter 4

Measuring angles in degrees

How can I say how big an angle is, with a number?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Say a right angle is 90° and a full turn is 360°
  • Measure an angle with a protractor
  • Draw an angle of 60° with a protractor

We measure angles in degrees. The sign for degrees is °.

A right angle is 90°. A straight line is two right angles, so it is 180°.

A full turn goes all the way round. It is four right angles, so it is 360°.

A protractor measures angles. Most are a half circle with two scales of numbers.

Draw it first

Measure an angle with a protractor

  1. An angle made of two green lines that meet at a corner. Step 1 labels the corner. Step 2 puts a protractor on it, with its centre on the corner and its 0 line along the right hand line. The outer scale reads 0, 30, 60, 90, 120, 150 and 180 from the right. The inner scale reads 180, 150, 120, 90, 60, 30 and 0. Step 3 labels the angle 60° and marks the outer scale from 0 to the second line.corner

    1 Find the corner of the angle. Its two arms are the lines.

  2. An angle made of two green lines that meet at a corner. Step 1 labels the corner. Step 2 puts a protractor on it, with its centre on the corner and its 0 line along the right hand line. The outer scale reads 0, 30, 60, 90, 120, 150 and 180 from the right. The inner scale reads 180, 150, 120, 90, 60, 30 and 0. Step 3 labels the angle 60° and marks the outer scale from 0 to the second line.corner01803015060120909012060150301800

    2 Put the centre of the protractor on the corner. Put its 0 line along one arm.

  3. An angle made of two green lines that meet at a corner. Step 1 labels the corner. Step 2 puts a protractor on it, with its centre on the corner and its 0 line along the right hand line. The outer scale reads 0, 30, 60, 90, 120, 150 and 180 from the right. The inner scale reads 180, 150, 120, 90, 60, 30 and 0. Step 3 labels the angle 60° and marks the outer scale from 0 to the second line.corner0180301506012090901206015030180060°

    3 Read the scale that starts at 0 on that arm. Here it says 60°.

There are two scales. Read the one that starts at 0 on your arm.

Check your number. Ask: is the angle smaller than a right angle? If it is, the number must be less than 90.

Worked example

Draw an angle of 60°.

  1. Draw a line with a ruler. Mark a dot on it for the corner.
  2. Put the centre of the protractor on the dot. Put its 0 line along your line.
  3. Find 60 on the scale that starts at 0 on your line. Mark a dot there.
  4. Take the protractor away. Join the corner to the new dot.
  5. Check: the angle should be smaller than a right angle.

Answer: An angle of 60°. It is smaller than a right angle.

The angle you drew. Two green lines meet at a corner, labelled corner. An arc between them is labelled 60°.corner60°
The angle after step 4. It is smaller than a right angle.

See it three ways

With things

Face a wall. Turn right by a quarter turn, four times. You are back where you began.

As a picture

Three turns. A quarter turn is a right angle, marked with a small square, labelled 90°. A half turn goes from one side of a straight line to the other, labelled 180°. A full turn goes all the way round a circle, labelled 360°.90°180°360°

In symbols

90° + 90° = 180°. 4 × 90° = 360°.

Try it

Make angles with no protractor

You need: your right angle tester, 3 sticks or strips of paper of the same length, a pencil and paper.

  1. Fold your tester so one arm lies on the other.
  2. The new corner is 45°. It is half of 90°.
  3. Lay it twice in a right angle. Two fit exactly.
  4. Lay 3 equal sticks end to end to make a triangle.
  5. Each corner of this triangle is 60°. Draw round one corner.
  6. Is 60° bigger or smaller than 45°? Is it smaller than 90°?

What you will see: Two 45° corners fill a right angle. The 60° corner is bigger than 45° and smaller than 90°.

If you cannot try it, this is what happens.
Two angles. The first is 45°, labelled folded tester. The second is 60°, labelled equal sticks.45°folded tester60°equal sticks

A wrong idea many people have

You can read an angle from either scale on a protractor.

Why it feels right: Both scales have the same numbers, so either one looks right.

The test that breaks it: Look at the 60° angle in the picture. It is smaller than a right angle. So its number must be less than 90.

What is true: Read the scale that starts at 0 on your arm. Then check it against a right angle.

Key words

degrees
the unit we use to measure an angle. It is written °.
full turn
all the way round. It is 360°.
protractor
a tool with a scale for measuring angles.

Back to your guess

The answer is B: Count how many degrees it turns, with a protractor.

We measure angles in degrees. A protractor shows how many degrees an angle turns.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. How many degrees are in 2 right angles?

    See the answer

    180°

    A right angle is 90°. 2 × 90° = 180°. That is a straight line.

  2. The 0 line of the protractor lies along the right hand arm. What is the angle?

    A protractor with its centre on the corner of an angle and its 0 line along the right hand green line. The other green line crosses the outer scale one small mark after 30.01803015060120909012060150301800
    Tap your answer.

    1. Yes, that is right. The scale starts at 0 on the right hand arm. The other arm is one small mark after 30. So it is 40°.

    2. Not this one. You read the other scale. This angle is smaller than a right angle. It must be less than 90°. Try another.

    3. Not this one. You counted the 30 mark as a step. Start at 30. The arm is one small mark on, so add 10 once: 40°. Try another.

    See the answer

    40°

    The scale starts at 0 on the right hand arm. The other arm is one small mark after 30. So it is 40°.

    • If you chose B: You read the other scale. This angle is smaller than a right angle. It must be less than 90°.
    • If you chose C: You counted the 30 mark as a step. Start at 30. The arm is one small mark on, so add 10 once: 40°.

  3. Joseph turns a quarter turn. Then he turns a half turn. How many degrees has he turned in all?

    See the answer

    270°

    A quarter turn is 90°. A half turn is 180°. 90° + 180° = 270°.

  4. You fold a right angle in half to make a 45° corner. How many of these corners fill one right angle?

    See the answer

    2

    90° ÷ 45° = 2. Two 45° corners fill a right angle.

  5. Draw an angle of 60° with a protractor. Is it acute or obtuse?

    See the answer

    It is acute. 60° is smaller than a right angle.

    An acute angle is smaller than 90°. 60° is less than 90°.

  6. From an earlier chapter

    An angle is 120°. Is it acute, a right angle or obtuse?

    Tap your answer.

    1. Not this one. Acute angles are smaller than 90°. 120° is more than 90°. Go to M2.5.3. Try another.

    2. Not this one. A right angle is exactly 90°. 120° is bigger. Go to M2.5.3. Try another.

    3. Yes, that is right. An obtuse angle is bigger than 90° and smaller than 180°. 120° is in between.

    See the answer

    Obtuse

    An obtuse angle is bigger than 90° and smaller than 180°. 120° is in between.

    • If you chose A: Acute angles are smaller than 90°. 120° is more than 90°. Go to M2.5.3.
    • If you chose B: A right angle is exactly 90°. 120° is bigger. Go to M2.5.3.

  7. Ana turns all the way round, to face the way she began. How many degrees has she turned?

    Tap your answer.

    1. Not this one. That is a half turn. After 180° she would face the opposite way. Try another.

    2. Not this one. That is a quarter turn, one right angle. All the way round is four of them. Try another.

    3. Yes, that is right. All the way round is four right angles. 4 × 90° = 360°.

    See the answer

    360°

    All the way round is four right angles. 4 × 90° = 360°.

    • If you chose A: That is a half turn. After 180° she would face the opposite way.
    • If you chose B: That is a quarter turn, one right angle. All the way round is four of them.

  8. The 0 line of the protractor lies along the right hand arm. What is the angle?

    A protractor with its centre on the corner of an angle and its 0 line along the right hand green line. The other green line crosses the outer scale one small mark after 120.01803015060120909012060150301800
    Tap your answer.

    1. Not this one. You read the other scale. This angle is bigger than a right angle. It must be more than 90°. Try another.

    2. Yes, that is right. The scale starts at 0 on the right hand arm. The other arm is one small mark after 120. So it is 130°.

    3. Not this one. You stopped at the last number you could see. The arm is one small mark after it. Try another.

    See the answer

    130°

    The scale starts at 0 on the right hand arm. The other arm is one small mark after 120. So it is 130°.

    • If you chose A: You read the other scale. This angle is bigger than a right angle. It must be more than 90°.
    • If you chose C: You stopped at the last number you could see. The arm is one small mark after it.

  9. Ravi draws a line and a corner dot. The protractor centre is on the dot. Its 0 is on his line. Which mark does he join to the dot to make 60°?

    A protractor with its centre on a corner. A green line, labelled his line, runs from the corner along the 0 line to the right. The corner is labelled corner. The outer scale reads 0, 30, 60, 90, 120, 150 and 180 from the right. The inner scale reads 180, 150, 120, 90, 60, 30 and 0.01803015060120909012060150301800cornerhis line
    Tap your answer.

    1. Yes, that is right. His line lies along 0 on the outer scale. It counts up from 0 on his line. So he joins its 60.

    2. Not this one. That scale starts at 0 on the left. From his line it is 120°, not 60°. Try another.

    3. Not this one. You counted 60° down from the 90° mark. Count 60° up from 0 on his line. Try another.

    See the answer

    The 60 on the outer scale

    His line lies along 0 on the outer scale. It counts up from 0 on his line. So he joins its 60.

    • If you chose B: That scale starts at 0 on the left. From his line it is 120°, not 60°.
    • If you chose C: You counted 60° down from the 90° mark. Count 60° up from 0 on his line.

  10. Look at the two angles. Which one is bigger?

    Two angles side by side. Angle P has short arms and opens wide. Angle Q has long arms and opens narrow. They are labelled angle P and angle Q.angle Pangle Q
    Tap your answer.

    1. Not this one. Long arms do not make a bigger angle. What counts is how far the angle opens. Try another.

    2. Yes, that is right. Angle P opens wider than angle Q. Angle size is how far an angle turns. Arm length does not matter.

    3. Not this one. Arm length does not change an angle, but these two open differently. One opens wider. Try another.

    See the answer

    Angle P

    Angle P opens wider than angle Q. Angle size is how far an angle turns. Arm length does not matter.

    • If you chose A: Long arms do not make a bigger angle. What counts is how far the angle opens.
    • If you chose C: Arm length does not change an angle, but these two open differently. One opens wider.

Keep it

Copy this into your exercise book.

A right angle is 90°. A straight line is 180°. A full turn is 360°. Put the protractor centre on the corner. Put its 0 line on one arm. Read the scale from 0.

Draw: A protractor with a 60° angle. Mark where you read the number.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

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