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 360^o.

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
180^o.

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 90^o.

Classification of angles

Angles are classified according to their size.

We say that

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

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 90^o are called complementary. For example, 23^o and 67^o 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 180^o are called supplementary angles. For example, 45^o and 135^o are supplementary angles.