# 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 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 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

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. :4 = 