Shape & Space
Understanding and Measuring Angles
3rd Class · 4th Class · 5th Class · 6th Class
- ✓Identify and name right, acute, and obtuse angles.
- ✓Understand that an angle is a measure of turn or the space between two lines that meet.
- ✓Accurately measure angles using a protractor.
- ✓Estimate the size of angles.
Key concepts
An angle is formed when two straight lines meet at a point. This point is called the vertex. The lines are called arms. Angles tell us how much 'turn' there is between the two lines. We measure angles in units called degrees, using the symbol °.
A right angle is an angle that measures exactly 90°. It looks like a perfect 'L' shape or the corner of a square. We often mark a right angle with a small square symbol at the vertex.
An acute angle is an angle that measures less than 90°. Think of it as a 'cute little' angle, smaller than a right angle.
An obtuse angle is an angle that measures more than 90° but less than 180°. It is wider than a right angle but not a straight line.
A protractor is a mathematical tool used to measure angles. It is usually a semi-circular (half-circle) or full-circular shape with degree markings around its edge. It has a centre point and two scales (inner and outer) for measuring.
Key facts to remember
- 1An angle is formed by two lines meeting at a vertex.
- 2Angles are measured in degrees (°).
- 3A right angle measures exactly 90°.
- 4An acute angle measures less than 90°.
- 5An obtuse angle measures more than 90° but less than 180°.
- 6A protractor is used to measure angles.
- 7When using a protractor, place its centre on the angle's vertex and one arm along the 0° line.
- 8Always read the scale that starts from 0° along the aligned arm.
Worked examples
Example 1
Look at the angle below. What type of angle is it? (Imagine an angle clearly smaller than 90°)
Answer
This is an acute angle.
An acute angle is always less than 90°.
Example 2
Measure the angle shown using your protractor. (Imagine an angle of 60°)
Answer
The angle measures 60°.
Always start measuring from the 0° mark on the scale that aligns with one of the angle's arms.
Example 3
Measure the angle shown using your protractor. (Imagine an angle of 135°)
Answer
The angle measures 135°.
An obtuse angle will always be greater than 90°. Make sure your measurement reflects this.
Common mistakes
- ✗Confusing acute angles with obtuse angles.
- ✗Reading the wrong scale on the protractor (e.g., reading the inner scale when the outer scale should be used, or vice versa).
- ✗Not placing the protractor's centre point exactly on the angle's vertex.
- ✗Not aligning one arm of the angle precisely with the 0° line of the protractor.
- ✗Measuring the larger angle around the vertex instead of the smaller interior angle.
Exam tips
- ★Always estimate the type and size of the angle first (e.g., 'It looks acute, so it should be less than 90°'). This helps catch errors.
- ★Use a sharp pencil to draw and mark angles clearly for accurate measurement.
- ★Double-check your protractor placement and reading before writing down your answer.
- ★Practice measuring different types of angles regularly to become confident.
Ready to practise?
Try a problem on this topic
Snap a photo or type a question — get step-by-step working instantly.