Angles
Types of angles
Angles are measured in degrees, and a right angle is the yardstick. Everything else is described as smaller, bigger, or bigger still.
Measuring turn in degrees
An ANGLE measures an amount of turn. It is measured in DEGREES, written °. A full turn is 360°. A half turn is 180°. A quarter turn is 90°. A quarter turn has a special name: a RIGHT ANGLE. It is usually marked with a small square rather than a curve.
The four types
ACUTE — less than 90°. A sharp, narrow angle. RIGHT ANGLE — exactly 90°. OBTUSE — more than 90° but less than 180°. REFLEX — more than 180° but less than 360°. So the order by size is: acute, right angle, obtuse, reflex.
Recognising a reflex angle
A reflex angle is the big one on the OUTSIDE. Whenever two lines meet they actually make two angles — a smaller one and a larger one — and the two add to 360°. If the smaller angle is 100°, the reflex angle on the other side is 360 − 100 = 260°. People often miss reflex angles because they only look at the inside.
Estimating without a protractor
Use the right angle as your ruler. Is it clearly less than a quarter turn? Acute. About a quarter turn? Around 90°. Between a quarter and a half turn? Obtuse — somewhere between 90° and 180°. More than half a turn? Reflex. Two right angles make 180°, three make 270°. Comparing with those landmarks gets you close.
Worked examples
Naming a 45° angle
- 45° is less than 90°.
- Angles smaller than a right angle are acute.
Answer: It is an acute angle
Naming a 130° angle
- 130° is more than 90° but less than 180°.
Answer: It is an obtuse angle
Naming a 250° angle
- 250° is more than 180° but less than 360°.
Answer: It is a reflex angle
Finding the reflex angle
- Two lines meet at 100°.
- The two angles round the point add to 360°.
- 360 − 100 = 260.
Answer: The reflex angle is 260°
Ordering angles by size
- Compare each with a right angle.
- Acute is under 90°, right angle is 90°, obtuse is 90°–180°, reflex is over 180°.
Answer: acute, right angle, obtuse, reflex
Where you see this in real life
- A door opened just a crack makes an acute angle; opened right back it makes a reflex angle.
- The corner of a book or a window frame is a right angle.
- A clock's hands make every kind of angle as the hours pass.
Key words
- Angle
- A measure of turn.
- Degree (°)
- The unit angles are measured in.
- Acute angle
- An angle smaller than 90°.
- Right angle
- An angle of exactly 90°, a quarter turn.
- Obtuse angle
- An angle between 90° and 180°.
- Reflex angle
- An angle between 180° and 360°.