### Topic Page: Angle

**angle**from

*The Hutchinson Unabridged Encyclopedia with Atlas and Weather Guide*

In mathematics, the amount of turn or rotation; it may be defined by a pair of rays (half-lines) that share a common endpoint (vertex) but do not lie on the same line. Angles are measured in degrees (°) or radians (rads or ^{c}) – a complete turn or circle being 360° or 2π rads.

All angles around a point on a straight line add up to 180°. All angles around a point add up to 360°.

Angles are classified generally by their degree measures: acute angles are less than 90°; right angles are exactly 90° (a quarter turn) and are created by two perpendicular lines crossing; obtuse angles are greater than 90° but less than 180° (a straight line); reflex angles are greater than 180° but less than 360°; supplementary angles add up to 180°.

Angles in triangles A triangle has three interior angles that together add up to 180°. In an equilateral triangle these angles are equal (60°). The exterior angles of a triangle (those produced if one side is extended beyond the triangle) are equal to the sum of the opposite internal angles.

Unknown angles in a right-angled triangle can be worked out using trigonometry.

Angles in polygons Regular polygons have three types of angle:

The angle at the centre is equal to the exterior angle and it is found by dividing 360° by the number of sides in the polygon.

For example, the angle at the centre of a hexagon is 60°:

360 ÷ 6 = 60°

Angles at parallel lines Angles created by a line crossing two parallel lines are known as opposite angles, corresponding angles, or alternate angles.

Angles in circles Angles within a circle can be calculated using circle theorems.

essays

Working out angles

weblinks

Ask Dr Math

CoolMath

Maths Year 2000

Dave's Short Trig Course

Discovery School's Webmath

Easymaths

Funbrain

Interactive Mathematics: Miscellany and Puzzles

Mathematics Lessons that Are Fun, Fun, Fun!

MATHguide

Maths for Morons Like Us

Maths Is Fun

Maths Online

Plus Magazine

Similar Triangles

SOS Mathematics: Trigonometry

StudyWeb

Trigonometry

images

alternate angles

angle

angles in triangles

### Images

### Video

### Related Credo Articles

##### angle

1. A measure of rotation about a fixed axis; commonly measured in degrees, radians, or revolutions. 2. The region between two rays...

##### angle

A configuration of two lines (the sides or arms ) meeting at a point (the vertex ). Often an angle is regarded as the measure of the...

##### Angle

What is algebra exactly; is it those three-cornered things? J. M. Barrie Nouns 1 angle bend, fork, corner, sharp...