angle

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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.

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