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 point. Angles are measured in degrees (°): a right angle is 90° and a full turn is 360°.
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 two lines are the arms of the angle, and the point where they meet is the vertex.
scissors
clock
pizza
Turns and degrees
Angles are measured in degrees, written with a small circle: 90°. A full turn, all the way around, is 360°.
| 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° |
Types of angle
- 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°.
Measuring with a protractor
- Put the protractor's center mark on the vertex.
- Line up the zero line with one arm.
- Read the scale that starts at 0 on that arm, where the other arm crosses it.
- Check the answer against your estimate: acute or obtuse?
Finding missing angles
Three facts let you work out 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° (see types of triangles). Inside any quadrilateral, they add up to 360°.
Worked example: two angles sit on a straight line and one is 115°. The other is 180° − 115° = 65°.
Examples
- A slice that is ⅛ of a round pizza has an angle of 360° ÷ 8 = 45°.
- A triangle with angles of 90° and 35° has a third angle of 180° − 125° = 55°.
- A quadrilateral with angles of 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. This is the most common mistake. 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?
Practise it
Try it
- Is a 200° angle acute, obtuse or reflex?
- Two angles on a straight line; one is 72°. What is the other?
- A triangle has angles of 40° and 75°. What is the third angle?
Answers: 1) Reflex. 2) 180° − 72° = 108°. 3) 180° − 115° = 65°.
Angle and geometry practice
Practise it step by step in a full course: Grade 6 Maths
For grown-ups
Related topics
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
3D shapes
3D shapes are solid shapes with length, width and height, like cubes, spheres, cylinders and pyramids. They have faces, edges and vertices.
Pythagoras' theorem
Pythagoras' theorem says that in a right-angled triangle, a² + b² = c², where c is the longest side (the hypotenuse). For sides 3 and 4, the hypotenuse is 5.
Symmetry
A shape has symmetry when one half is a mirror image of the other (line symmetry), or when it looks the same after being turned (rotational symmetry).
Parallel and perpendicular lines
Parallel lines run side by side and never meet, always the same distance apart. Perpendicular lines cross or meet at a right angle of exactly 90 degrees.
Polygons
A polygon is a flat shape made only of straight sides that close up completely. Triangles, squares, pentagons and hexagons are polygons; a circle is not.