Take an example of your arms. Let's say you want to give a hug to your friend. You will be opening your arms at a wide-angle for the hung. Basically, you are creating more space between your arms by increasing the distance from one arm to another. In short, you are widening your angle for the hug, so what is an angle? And how many types of angles are there? Let's talk about it.

An angle is a region of a plane between two rays that share a common origin. The rays are called arms and the common origin is the vertex. Take an example of the below diagram.

We have two lines, which are and b, and between both lines, there is an angle. The angle is showing the deviation of line a from line b. To measure angles, the unit degree (º) is most frequently used. Although, there are two more units of angles that are also used in other applications and they are radians and revolutions. Speaking of angles, there are different types of angles too.

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Types of Angles

Below is the list of all types of angles that are categorized according to their properties.

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

A 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.

Congruent Angles

Congruent angles have the same measure.

Adjacent Angles

Adjacent angles mean two angles that share 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 have a 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

 

When an intersecting transversal bisects through a pair of parallel lines, corresponding angles are formed. Corresponding angles are a pair of angles that are at the same relative position, however, their positioning is on different intersections. In the above diagram, angle 1 and angle 2 are equal because they are corresponding angles.

Alternate Interior Angles

 

The corresponding angle theorem is also applied here. In corresponding angles, we usually look at the same relative position, however, in alternate interior angles, angles are found on the opposite side of the transversal. In the above diagram, angle 2 and angle 3 are equal because they are alternate interior angles.

Alternate Exterior Angles

 

In the case of alternate exterior angles, angles are found outside after their lines (which are parallel) is intersected by the transversal. In the above diagram, angle 1 and angle 4 are equal because they are alternate exterior angles.

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.

Whole angle =

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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.