Acute
Greater than 0° but less than 90°.
Learning Objectives
- identify acute, right, obtuse, straight and reflex angles;
- name angles using three letters;
- measure and draw angles accurately;
- estimate angle size before measuring;
- recognise full turns and quarter turns.
Introduction
An angle measures the amount of turning between two rays that meet at a common point called the vertex.
Think about opening a door, turning a bicycle handlebar or moving the hands of a clock. In each case, the size of the turn can be described by an angle.
Angles are measured in degrees, written using the symbol °.
Key Notes
Right
Exactly 90°.
Obtuse
Greater than 90° but less than 180°.
Straight
Exactly 180°.
Reflex
Greater than 180° but less than 360°.
Full Turn
Exactly 360°.
Clean Angle Diagram
Naming an Angle
When using three letters, the vertex must be the middle letter. For example, ∠ABC has vertex B.
Common mistake: Writing the vertex as the first or last letter changes which angle is being named.
Interactive Learning: Build and Classify an Angle
Classification: acute angle
🧠 Let’s Think Together
An angle is larger than a right angle but smaller than a straight angle. What can you say about it before measuring it?
It must be an obtuse angle because its size lies between 90° and 180°. Classification is about comparing the turn with known benchmark angles.
Worked Examples
Example 1: Classify 128°
1
Compare 128° with 90° and 180°.
2
Since 90° < 128° < 180°, it is an obtuse angle.
Example 2: Name an angle
If rays BA and BC meet at B, the vertex is B. The angle is named ∠ABC or ∠CBA because the vertex letter must be in the middle.
Practice Questions
Foundation- Classify 35°, 90°, 145°, 180° and 275°.
- What angle is one quarter of a full turn?
- What angle is three quarters of a full turn?
- Find the smaller angle between the hands of a clock at 3 o'clock.
- An angle is 28° greater than a right angle. Classify it.
- A reflex angle is 70° more than a straight angle. Find the angle.
✅ Check Your Work
Show practice answers
- Acute, right, obtuse, straight and reflex.
- 90°.
- 270°.
- 90°.
- 118°, which is obtuse.
- 250°.
Common Mistakes
- Calling every large-looking angle obtuse without checking whether it is greater than 180°.
- Putting the vertex anywhere other than the middle when naming an angle with three letters.
- Measuring from the wrong zero on a protractor.
Exam Focus
Use exact mathematical words and include the degree symbol. When naming an angle, check the vertex first. When measuring, estimate the angle type before reading the protractor scale.
Summary
- Acute < 90°.
- Right = 90°.
- Obtuse is between 90° and 180°.
- Straight = 180°, reflex is between 180° and 360°.