Maths
What is an angle?
Quick answer
An angle measures the amount of turn between two lines that meet at a point. Angles are measured in degrees (°); a right angle is 90° and a full turn is 360°.
In one sentence
An angle is the amount of turn between two lines that meet at a corner.
Explained
Open a pair of scissors a little and the blades make a small angle. Open them wide and the angle gets bigger. The length of the blades doesn't matter; only how far they have turned apart. The point where the two lines meet is the vertex.
scissors
clock
pizza
Angles are measured in degrees, written with a small circle: 90°. A full turn, all the way round, is 360°. That gives us some landmarks:
| Turn | Degrees | Name |
|---|---|---|
| quarter turn | 90° | right angle (marked with a little square) |
| half turn | 180° | straight line |
| three-quarter turn | 270° | |
| full turn | 360° |
Angles are also sorted by size:
- Acute: less than 90° (think "a cute little angle").
- Right: exactly 90°, like the corner of a book.
- Obtuse: between 90° and 180°.
- Reflex: between 180° and 360°.
You measure angles with a protractor. Line its centre cross up with the vertex and its zero line along one arm, then read where the other arm crosses the scale. Use the scale that starts at 0 on your arm; estimating first ("is it acute or obtuse?") stops you reading the wrong one.
Three facts let you work out missing angles without measuring:
- Angles on a straight line add up to 180°.
- Angles around a point add up to 360°.
- The angles inside any triangle add up to 180°. (Inside any quadrilateral, 360°.)
Examples
- A slice that is ⅛ of a round pizza has an angle of 360 ÷ 8 = 45°.
- On a straight line, if one angle is 115°, the other is 180 − 115 = 65°.
- A triangle with angles 90° and 35° has a third angle of 55°.
- A quadrilateral with angles 80°, 100° and 95° has a fourth of 360 − 275 = 85°.
- An equilateral triangle has three 60° angles.
Common mistakes
- Reading the wrong scale on a protractor, giving 120° for a 60° angle. Fix: decide first whether it is acute or obtuse.
- Thinking longer lines make a bigger angle. The angle is the turn, not the length.
- Forgetting reflex angles. Around a point, the "outside" angle is 360° minus the inside one.
Quick quiz
Angles
Check what you know with 5 quick questions.
Question 1 of 5
How many degrees are in a right angle?
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Angle and geometry practice
For grown-ups
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