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.
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