An angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.

The size of an angle

Imagine that the ray OB is rotated about the point O until it lies along OA. The amount of turning is called the size of the angle AOB.

A revolution is the amount of turning required to rotate a ray about its endpoint until it falls back onto itself. The size of 1 revolution is 360o.

A straight angle is the angle formed by taking a ray and its opposite ray. A straight angle is half of a revolution, and so has size equal to

Right angle

Let AOB be a line, and let OX be a ray making equal angles with the ray OA and the ray OB. Then the equal angles ∠AOX and ∠BOX are called right angles.

A right angle is half of a straight angle, and so is equal to 90o.

Classification of angles

Angles are classified according to their size.

We say that

  • An angle with size α is acute if 0o < α < 90o,
  • An angle with size α is obtuse if 900 < α < 180o,
  • An angle with size α is reflex if 1800 < α < 360o

Adjacent angles

Two angles at a point are called adjacent if they share a common ray and a common vertex and lie on opposite sides of the common ray.

Hence, in the diagram,

  • AOC and ∠BOC are adjacent

Two angles that add to 90o are called complementary. For example, 23o and 67o are complementary angles.

In each diagram the two marked angles are called corresponding angles.

If the lines are parallel, then each pair of corresponding angles are equal.

Conversely, if a pair of corresponding angles are equal, then the lines are parallel.

Two angles that add to 180o are called supplementary angles. For example, 45o and 135o are supplementary angles.