Geometry
Angles: Measuring, Drawing, and Properties
Year 3 · Year 4 · Year 5 · Year 6
- ✓By the end of this lesson students will be able to identify and name different types of angles (acute, obtuse, right, straight, reflex).
- ✓By the end of this lesson students will be able to measure angles accurately using a protractor.
- ✓By the end of this lesson students will be able to draw angles of a given size using a protractor.
- ✓By the end of this lesson students will be able to understand and apply the properties of angles on a straight line and around a point.
- ✓By the end of this lesson students will be able to understand and apply the property of angles in a triangle.
Key concepts
An angle is formed when two straight lines meet at a point. This point is called the vertex, and the lines are called arms. Angles are measured in units called degrees (°).
Angles are classified by their size: - A **right angle** is exactly 90°. It is often shown with a square symbol. - An **acute angle** is less than 90°. - An **obtuse angle** is greater than 90° but less than 180°. - A **straight angle** (or angles on a straight line) is exactly 180°. - A **reflex angle** is greater than 180° but less than 360°. - A **full turn** (or angles around a point) is exactly 360°.
To measure an angle, you use a protractor. Place the centre of the protractor exactly on the vertex of the angle. Line up one arm of the angle with the 0° line on the protractor. Read the scale where the other arm crosses the protractor. Remember to choose the correct scale (inner or outer) depending on which 0° line you started from.
To draw an angle, first draw a straight line (this will be one arm of your angle). Mark a point on one end of this line (this will be your vertex). Place the centre of your protractor on the vertex and line up the drawn line with the 0° mark. Find the desired angle measurement on the protractor and make a small mark. Remove the protractor and use a ruler to draw a straight line from the vertex to your mark. This forms the second arm of your angle.
Angles that lie on a straight line always add up to 180°. This is because a straight line itself represents a half turn.
Angles that meet at a single point and form a full circle (or full turn) always add up to 360°.
The three interior angles inside any triangle always add up to 180°.
Key facts to remember
- 1A full turn is 360°.
- 2Angles on a straight line add up to 180°.
- 3A right angle is exactly 90°.
- 4The angles inside any triangle add up to 180°.
- 5Acute angles are less than 90°.
- 6Obtuse angles are greater than 90° but less than 180°.
- 7Reflex angles are greater than 180° but less than 360°.
- 8Always use a protractor to measure and draw angles accurately.
Worked examples
Example 1
Find the missing angle 'x' on the straight line below:
Answer
x = 115°
Always state the reason for your calculation (e.g., 'angles on a straight line').
Example 2
Calculate the missing angle 'y' around the point below:
Answer
y = 150°
Remember that a square symbol indicates a right angle (90°).
Example 3
Find the missing angle 'z' in the triangle below:
Answer
z = 60°
This rule applies to all types of triangles.
Common mistakes
- ✗Reading the wrong scale on a protractor (e.g., inner instead of outer, or vice versa).
- ✗Not placing the protractor's centre exactly on the vertex of the angle.
- ✗Confusing acute angles (less than 90°) with obtuse angles (greater than 90°).
- ✗Incorrectly assuming an angle is 90° without the right angle symbol.
- ✗Forgetting that angles on a straight line add to 180° or that angles in a triangle add to 180°.
Exam tips
- ★Always use a sharp pencil and a clear protractor for accuracy when measuring or drawing.
- ★After calculating a missing angle, check if its size looks reasonable (e.g., if it should be acute, does your answer reflect that?).
- ★Show all your working steps clearly, including the mathematical reason for your calculation (e.g., 'angles on a straight line = 180°').
- ★Look carefully for the square symbol, which always indicates a right angle (90°).
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