Angles

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Angles in Detail

Whenever two lines meet at a point, it forms an angle. The point where these lines meet is called a node or a vertex. The term "Angle" originated from the Latin "Angulus". If you look around, everything that is touching another surface is at some angle or the other.

Let's discuss the different types of angles, what they are called and how they are used in mathematics.


Definition of Angles

The most basic definition of an angle according to the Euclidean geometry is a figure that is formed by two rays sharing a common point. These two rays are on the same plane, and when an angle is formed due to the intersection of two lines it is called a dihedral angle.


An angle is represented with a value in degrees that spans from 0-360. Different values of degrees form different types of angle that have different names. A particular range of degrees has been assigned a specific name such as Obtuse angle, Right angle, Acute angle etc.


Definition of Angle in Math

There is only one definition of angle in mathematics that explains how one can measure and classify different angles. To understand this better, let's start from the fundamental aspects of an angle.


What is a Ray?

A ray is defined as a line that starts from a point and keeps extending from its other end. It is named after its starting point and another point on the line. It is represented as an arrow to show its ever-extending nature.


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What is a Vertex?

When two rays share a common starting point, it creates an angle, and that common point is called a vertex. An angle is represented by the symbol ∡. 

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Remember that the name denoting the vertex always remains in the middle while the other points can exchange positions.


Angle and Algebra

A graphical and coordinate-based approach is taken when representing an angle. The coordinate points help in solving equations related to angles by plotting the lines or rays on a coordinate plane.


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Types of Angles and Their Definitions

Definition of Straight Angle

An angle is said to be straight when the two rays are forming an angle of exactly 180 - degree. It is named so because two lines at a 180 - degree angle look like a single straight line.


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Definition of Acute Angles

When the angle between two lines is less than 90-degree, it is called an acute angle. Any angle between 0-90 degrees is an acute angle.


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Definition of Right Angle

When two rays form an angle of 90-degree, it is called a right angle. Among other kinds of angles, this particular angle is given comparatively more importance. An entire subject called Trigonometry is built upon this angle as most things around us form a right angle in respect with their surface.


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Definition of Obtuse Angle

The range of angles above 90-degree and below 180-degree is called an obtuse angle. One can think of it as the opposite of acute angle as well. 


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Definition of Reflex Angle

Any angle formed beyond 180 - degree is a reflex angle. However, this also has its limitation, and that is below 360. It is because when a line crosses 360-degree, it completes a full rotation and it again starts from 0-degree. 


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Definition of Adjacent Angle

When two angles share a common vertex and have a common side, it is called an adjacent angle. It should be noted that if both the criteria are not met, then it is not adjacent. The very meaning of adjacent angles is that two angles are side by side. Also, if one angle overlaps another, it is not an adjacent angle.


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Define Complementary Angles

Two angles are said to be complimentary when their sum is 90 degree. They don't need to share a common vertex or side, only the sum of their respective angle decides whether they are complementary or not.


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The picture above is an example of a complementary angle pair, but the image below also represents the meaning of complementary angles.


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Even though these two are sharing anything in common, the fact that 30 degree and 60 degree adds up to 90 degree makes them complementary. 

If you wish to learn more about angles and how to solve its sums, start Vedantu's online classes today. Their live classes are both detailed and interesting, making learning maths fun. Go through their inventory full of sample sheets to gauge how much you know about this geometrical subject.

FAQ (Frequently Asked Questions)

1. What are all Angles Names?

Ans. A full rotation is of 360-degree, and anything in between is 1-360 degree is an angle. However, some specific ranges have been given a particular name. There are five primary types of angles, namely Acute, Obtuse, Straight, Right and Reflex.


However, there are five types of angles that are named defining the relationship between one angle with respect to another. These five angle names are Complementary, Adjacent, Congruent, Supplementary and Bisector.

2. What is a Bisector Angle?

Ans. It is said to be a bisector when two adjacent angles have equal values. It is not a bisector when the two angles do not have a common ray.

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For example, in the diagram above

∡AOB has a line OC tat is bisecting it from the middle. It is a bisector angle because

∡AOC = ∡COB

Note that a bisector angle that divides 90-degree into two 45-degree angles is both complementary and adjacent angle as well. 


3. What is the Angle Definition Geometry?

Ans. In geometry, an angle is a shape that is formed when two rays or lines diverge from a common point called its vertex. An angle is represented with the sign ∡ and has a certain degree that ranges from 1 - 360. Apart from the vertex, its other attributes are its two legs (lines), its interior and exterior. The interior is the part within the 'jaws' of the two lines while all the space that is not within it is the exterior.