# Angles

An **angle** is the region of a plane between two rays that share a common origin. The rays are called **arms** and the common origin is the **vertex**.

To measure angles, the unit degree (º) is most frequently used.

## Types of Angles

#### Acute Angle

An **acute angle** measures between **0º** and **90º**.

#### Right Angle

A **right angle** measures exactly **90º**.

#### Obtuse Angle

An **obtuse angle** measures between **90º** and **180º**.

#### Straight Angle

A **straight angle** measures exactly **180º**.

#### Reflex Angle

An **reflex angle** measures between **180º** and **360º**.

#### Negative Angle

A **negative angle** measures **less than 0º**.

Negative angles rotate in a clockwise direction.

A negative angle can be transformed into a positive angle by adding 360º to it.

−30º = 360º − 30º = **330º**

#### Congruent Angles

**Congruent angles** have the **same measure**.

#### Adjacent Angles

**Adjacent angles** have a **common side** and a common **vertex**.

#### Complementary Angles

**Complementary angles sum 90°**.

#### Supplementary Angles

**Supplementary angles sum 180°**.

#### Vertical Angles or Opposite Angles

The vertical angles share the common vertex and the sides of one are an extension of the sides of the other.

The angles 1 and 3 are equal.

The angles 2 and 4 are equal.

#### Corresponding Angles

The angles 1 and 2 are equal.

#### Alternate Interior Angles

The angles 2 and 3 are equal.

#### Alternate Exterior Angles

The angles 1 and 4 are equal.

## Operations with Angles

### Adding Angles

The sum of two angles is another angle whose amplitude is the sum of the amplitudes of the two initial angles.

### Subtracting Angles

The subtraction of two angles is another angle whose amplitude is the difference between the amplitude of the higher angle and the lower angle.

### Multiplying an Angle by a Number

Multiplying a number by an angle is another angle whose amplitude is the amplitude of the angle multiplied by as many times as specified by the number.

### Dividing an Angle by a Number

The division of an angle by a number is another angle that is multiplied by this number and gives the original angle.

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