Types of angles

Do you need know what type of angle it is one in particular and calculate its supplementary or complementary? Use our online calculator and you will get the result you are looking for immediately. Just type the amplitude of the angle in degrees and click the calculate button to find out its classification.

If you want to learn more about the types of angles that exist on the basis of their measure, their sum, their position or other criteria. Read on because here you will find all the information you are looking for.




Angle classes according to their measure

The first classification of angles that we are going to see is based on their size. Below is a table that summarizes the types of angles based on their amplitude that we can measure in degrees or radians. If we need more precision, we can also convert the degree in degrees, minutes and seconds.

Angle typeMeasure
Null
AcuteLess than 90º.
Right90º
ObtuseMore than 90º and less than 180º.
Straight180º
Complete360º
ConvexBetween 0º and 180º.
ConcaveBetween 180º and 360º.

In case you have any doubts, we will now look at each type of angle according to its size in a little more detail.

Null angle

The null angle is the angle that is worth 0º. and is formed by two coincident ray lines, which causes its aperture to be zero.

Acute angle

List of acute angles

The acute angle is the angle that has an amplitude between 0º and 90º. or between 0 and π/2 if expressed in radians.

Right angle

Right angle

A right angle is an angle that is exactly 90 degrees or π/2 radians. It is a very well known angle in trigonometry since it is present in the Pythagorean TheoremYou will be working with him frequently.

Pythagorean Theorem

When we encounter a right angle, a kind of box is usually drawn on the corner (you have it represented in red in the image above). This box is only drawn with the angles that have 90º so it is a way to identify them quickly.

Obtuse angle

Obtuse angles

An obtuse angle is defined as an angle having an amplitude of greater than 90º but less than 180º.. If we speak in radians, its measure is greater than π/2 radians but less than π radians.

Straight angle

Straight angle

There is not much to say about the straight angles since measure exactly 180º. or π radians. In some places the straight angle is referred to as extended but this is an infrequent designation.

Full angle

Full angle

We define full angle as that whose amplitude is 360º or 2π radians. In short, a complete circle around.

Concave and convex angles

Concave and convex angles

There are always doubts about concave and convex angles since we do not usually remember which one is which.

  • Convex angle: measures between 0º and 180º (between 0 and π radians).
  • Concave anglemeasures more than 180º but less than 360º.

As you can see, both are classified according to their size with respect to the straight angle (180º). If it is less than this it will be convex due to the type of curvature while if it is greater it will be concave.

Types of angles according to their sum

The second classification of angles that we are going to see is based on the sum of two angles. Depending on the value that the sum gives us, we will have supplementary or complementary angles:

Supplementary angles

Supplementary angles

They are two angles that when added together give us 180º.. Let's take a look at several examples:

  • The supplementary angle of 30º is 150º.
  • The supplementary angle of 123 degrees is 57º.
  • The 45º supplementary is 135º.

From the above we can deduce that two angles are supplementary if:

  • Both measure 90º or are right angles.
  • One is obtuse (measuring more than 90º) and the other is acute (less than 90º).

How do we find the supplementary angle of another of which we know its value? We simply have to solve the following formula:

Supplementary angle = 180º - α

Where α is the amplitude in degrees of the angle we know.

Complementary angles

complementary angles

Two complementary angles are those that when added together give us 90º.. For example:

  • The complementary angle of 30º is 60º.
  • The complementary of 35º is 55º.
  • The complementary angle of 120º is -30º.

The formula to find the complementary angle of another is as follows:

Complementary angle = 90º - α

Types of angles according to their position

Adjacent angles

Adjacent angles

Adjacent angles with those that meet the following characteristics:

  • They have one side and the vertex in common
  • The other side is on the same straight line.

For the above requirements, adjacent angles are always supplementary angles (add up to 180º) and consecutive.

Consecutive angles

consecutive angles

Consecutive angles have the following characteristics:

  • They have one side and the vertex in common
  • The other side does not lie on the same straight line, so they are not supplementary angles (do not add up to 180 degrees)

Vertically Opposite Angles

Vertically Opposite Angles

The vertically opposite angles are those that have their sides located on the same straight lines and these intersect at the vertex they have in common. In this way

  • α = β
  • θ = φ

In this type of angles you have to know that:

α + β + θ + θ + φ = 360º.

But if we take into account the equalities we have seen before, the equation can be simplified as follows:

2α + 2θ = 360º.

2 (α + θ) = 360º.

α + θ = 180º.

Thanks to the previous demonstration we can see that both angles are supplementary and we can find the value of one of them if we know the value of the other.

Angles between parallels and a transversal straight line

There is a third classification of angles that we have when there are two parallel lines and a transversal line passing through themforming a total of 8 angles that we can classify in different ways depending on their position.

Corresponding angles

corresponding angles

We call corresponding angles those that have the same position with respect to the transversal line, which also makes them have the same measure or amplitude.

In the case of the image, congruent angles would be those corresponding to the pairs:

  • 1 y 5
  • 3 y 7
  • 4 y 8
  • 2 y 6

Alternate interior angles

Alternate interior angles

The alternate interior angles are those that lie within the region between the parallel lines. Again, several pairs of angles that are equal are generated:

  • 2 y 8
  • 3 y 5

Alternate exterior angles

Alternate exterior angles

The alternate exterior angles are those that are in the outer part of the region between the straight lines that are parallel. In this case, the following angles will be equal:

  • 4 y 6
  • 1 y 7

This is due to the Theorem of the alternate exterior angles and by which we can see that:

∠1 + ∠4 = 180º

∠6 + ∠7 = 180º

We equal both equations and we are left with the following:

∠1 + ∠4 = ∠6 + ∠7

If we solve, we can see that angles 4 and 6 are equal, something that also happens between angles 1 and 7.

If you have any doubts about the types of angles that exist or you know more classifications that you want us to add, leave us a comment and we will help you as soon as possible.

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