Angles
Acute and obtuse angles
Angles have special names based on their size. In this unit you learn about right angles, acute angles and obtuse angles.
The right angle
A right angle is exactly 90 degrees (90°). It is the angle of a quarter turn, like the corner of a square. Two right angles together make 180° — a straight line.
Acute angles
An acute angle is less than 90° — it is less than a right angle. Angles like 30°, 45° and 80° are all acute. They look 'sharp' and narrow.
Obtuse angles
An obtuse angle is: • more than 90° (more than a right angle), and • less than 180° (less than two right angles). Angles like 100°, 135° and 150° are all obtuse. They look 'wide' and open.
Naming an angle
To name an angle, compare it to a right angle: • If it is less than 90°, it is acute. • If it is exactly 90°, it is a right angle. • If it is more than 90° but less than 180°, it is obtuse.
Worked examples
Naming a right angle
- The angle is exactly 90°.
- That is the angle of a quarter turn.
Answer: It is a right angle.
Is this angle acute?
- The angle measures 45°.
- 45° is less than 90°.
- Less than a right angle means acute.
Answer: 45° is an acute angle.
Is angle X acute or obtuse?
- Angle X is greater than a right angle, so it cannot be acute.
- Angle X is less than two right angles (180°).
- More than 90° and less than 180° means obtuse.
Answer: Angle X is obtuse.
Where you see this in real life
- The square corner of a book or a table is a right angle.
- The narrow point of a slice of pizza is an acute angle.
- A reclining deck-chair leans back at an obtuse angle.
Key words
- Right angle
- An angle of exactly 90°, the angle of a quarter turn.
- Acute angle
- An angle less than 90°.
- Obtuse angle
- An angle more than 90° but less than 180°.
- Straight line
- Two right angles together — an angle of 180°.