Year 6 Maths: Measuring Angles

Introduction to Angles

Hello, Year 6! Today we are going to learn about measuring angles. An angle is formed when two lines meet at a point. This point is called the vertex, and the lines are called arms.

What is an Angle?

• Angle: The space between two lines that meet at a point.
• Vertex: The point where the two lines meet.
• Arms: The two lines that create the angle.

Measuring Angles

To measure an angle, we use a tool called a protractor. A protractor is a semi-circular tool marked with degrees (°).

Steps to Measure an Angle with a Protractor:

1. Place the Protractor: Position the midpoint (the small hole or line) of the protractor at the vertex of the angle.
2. Align the Base Line: Make sure one arm of the angle lines up with the zero line on the protractor.
3. Read the Measurement: Look at where the other arm crosses the numbered scale of the protractor. That number tells you the size of the angle in degrees.

Types of Angles

• Acute Angle: Less than 90°
• Right Angle: Exactly 90°
• Obtuse Angle: More than 90° but less than 180°
• Straight Angle: Exactly 180°

Key Rules

• Always start measuring from the vertex.
• Make sure to use the correct scale (inside or outside) depending on how the angle is drawn.
• Remember the types of angles to help you identify them!

Tips and Tricks

• Use a ruler to draw straight lines before measuring.
• Practice measuring different angles to get better at it!
• Remember: If you have a triangle, the sum of all its angles is always 180°.

Practice Questions

Easy Level Questions

1. What is the angle called when it is exactly 90°?
2. How do you measure an angle using a protractor?
3. What type of angle is less than 90°?
4. What is the vertex in an angle?
5. If an angle measures 45°, what type of angle is it?
6. What is an obtuse angle?
7. Draw an angle that measures 30°.
8. What tool do we use to measure angles?
9. How many degrees are in a straight angle?
10. If an angle measures 120°, what type of angle is it?
11. Draw a right angle.
12. What do you call the two lines that form an angle?
13. True or False: A 75° angle is an acute angle.
14. If one arm of the angle is at 0°, where should you look to measure the angle?
15. How many degrees are in a full circle?
16. What is the smallest angle you can measure?
17. Can an angle measure 100° and still be acute?
18. What is the difference between an acute and obtuse angle?
19. If an angle is 180°, what is it called?
20. Draw an obtuse angle.

Medium Level Questions

1. Measure the angle below using a protractor. (Provide a drawing)
2. If you have a triangle with angles of 50° and 60°, what is the third angle?
3. Which is larger, a right angle or an obtuse angle?
4. Draw an angle that measures 135°.
5. If an angle measures 70°, what type of angle is it?
6. Explain why the sum of angles in a triangle equals 180°.
7. Measure the following angle: (Provide a drawing)
8. Can an angle be negative? Why or why not?
9. If two angles add up to 90°, what are they called?
10. What do you call an angle that measures more than 180°?
11. Draw a straight angle and label the vertex.
12. If angle A is 45° and angle B is 45°, what is angle C if they form a straight line?
13. Measure the angle below and write down your answer. (Provide a drawing)
14. How would you describe a 95° angle?
15. What is the complementary angle of a 30° angle?
16. What type of angle is 180°?
17. If an angle is 60°, what is its supplement?
18. Draw a triangle and label all angles.
19. Measure the angle below using a protractor. (Provide a drawing)
20. If an angle measures 20°, what is the complementary angle?

Hard Level Questions

1. A triangle has angles of 70° and 80°. Calculate the third angle.
2. Measure the angle formed by the hands of a clock at 3 o’clock.
3. If two angles are complementary and one measures 35°, what does the other angle measure?
4. Draw a right triangle and label all angles.
5. If an angle is 150°, what is its supplementary angle?
6. Measure a reflex angle and explain what makes it reflex. (Provide a drawing)
7. A polygon has five sides. What is the sum of its interior angles?
8. How do you find the measure of an exterior angle of a triangle?
9. Explain the difference between acute, right, and obtuse angles with examples.
10. Measure the angle below using a protractor and explain your process. (Provide a drawing)
11. If angle A is 120° and angle B is 30°, what type of angle is formed when they meet?
12. What is the relationship between complementary and supplementary angles?
13. If you have a circle, what is the angle at its center for one quarter of the circle?
14. An angle measures 210°. What type of angle is it?
15. Calculate the angles of a hexagon.
16. Measure the angle of a triangle that has sides measuring 7 cm, 8 cm, and 9 cm.
17. If an angle measures 75°, what is the measure of its supplementary angle?
18. Draw a circle and divide it into 8 equal angles. What is the measure of each angle?
19. If you have an angle measuring 45° and you double it, what angle do you get?
20. How can you tell if an angle is a right angle without using a protractor?

Answers and Explanations

Easy Level Answers

1. Right angle
2. Use a protractor to measure from the vertex.
3. Acute angle
4. The point where the two lines meet.
5. Acute angle
6. An angle more than 90° but less than 180°.
7. (Students should draw 30°)
8. Protractor
9. 180°
10. Obtuse angle
11. (Students should draw a right angle)
12. The two lines that form an angle.
13. True
14. Look at the number where the other arm crosses.
15. 360°
16. 0°
17. No, it cannot be negative.
18. An acute angle is smaller than an obtuse angle.
19. Straight angle
20. (Students should draw an obtuse angle)

Medium Level Answers

1. (Students should measure the angle provided)
2. 70° (180° – 50° – 60° = 70°)
3. An obtuse angle is larger than a right angle.
4. (Students should draw a 135° angle)
5. Acute angle
6. The angles in a triangle always add up to 180°.
7. (Students should measure the angle provided)
8. Angles cannot be negative as they measure space.
9. They are called complementary angles.
10. It is called a reflex angle.
11. (Students should draw a straight angle)
12. 90° is complementary, and 180° is supplementary.
13. 90°
14. An obtuse angle
15. 60° (90° – 30°)
16. 120° (180° – 60°)
17. 90° (180° – 60°)
18. (Students should draw a triangle)
19. (Students should measure the angle provided)
20. 70° (90° – 20°)

Hard Level Answers

1. 30° (180° – 70° – 80°)
2. 90° (3 o’clock is a right angle)
3. 55° (90° – 35°)
4. (Students should draw a right triangle)
5. 30° (180° – 150°)
6. (Students should measure and explain a reflex angle)
7. 540° (Sum of angles = (n – 2) x 180°; n = 5)
8. The exterior angle equals the sum of the two opposite interior angles.
9. Acute is less than 90°, right is exactly 90°, and obtuse is more than 90°.
10. (Students should measure and explain their process)
11. They form an obtuse angle.
12. Complementary angles add to 90°, and supplementary angles add to 180°.
13. 90° for one quarter of the circle.
14. Reflex angle
15. 720° ((n – 2) x 180°; n = 6)
16. (Students should measure the angles using the triangle sides)
17. 105° (180° – 75°)
18. 45° each (360° ÷ 8)
19. 90° (2 x 45°)
20. Use a square or check if it forms two 45° angles.

I hope you enjoyed learning about angles today! Remember, practice makes perfect!