### Angle

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 90^{0}< α < 180^{o}, - An angle with size α is
**reflex**if 180^{0}< 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.