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Angles (Mathematics Glossary)

What Is an Angle?

An angle is created by two rays that have a common end point, called the vertex.

an angle

The angle is also a measure of the rotation between the two rays.

Angles can be measured in degrees (°) or in radians.

How to Identify an Angle

Angles are often identified using Greek letters (α, β, γ, θ, ψ). The letter theta θ is often used.

angle theta

In geometric figures, points are often labelled with capital letters. Consider the angle made between points ABC, where the vertex is A and AB and AC are the rays:

ABC

The angle can be identified as the angle A, or by ∠BAC, where the middle of the 3 letters is the vertex.

How to Measure an Angle

An angle is measured by the shortest rotation between the two rays.

Angles are often measure in degrees, denoted °. There are 360 degrees in a full rotation.

Angles can also be measured in radians. There are 2π radians in a full rotation.

Angles can be measured directly using a protractor:

Angles can also be calculated using geometry and trigonometry.

Types of Angles

The different types of angles are:

Type of Angle Description
Acute Less than 90°
Right 90°
Obtuse Greater than 90° but less than 180°
Straight 180°
Reflex Greater than 180°
Full 360°

Read more about the types of angles

Curriculum
Geometry Lessons
Interactive Test
  show
 

Here's a second test on angles.
Here's a third test on angles.

Note

Parts of an Angle

parts of an angle explained

An angle is created by two rays meeting at a common endpoint, the vertex.

  • A ray is a line which starts from a point.

  • A vertex is the point where the two rays meet.

What's in a Name?

Angle comes from the Latin word 'angulus' meaning "corner".

It has the same root as the word "ankle", because the foot forms a corner with the leg.

an angle in an ankle