There are various types of angles in geometry. Angles form the core of the geometry in mathematics. They are the fundamentals that eventually lead to the formation of the more complex geometrical figures and shapes. Lets us begin with the study of different types of angles in maths to get a better understanding of the topic.
When two rays combine with a common end point and the angle is formed. The two components of an angle are “sides” and “vertex”. The side can be categorized into terminal sides and initial sides (or vertical sides) as shown in the image below.
These two rays can combine in multiple fashions to form the different types of angles in mathematics. Let us begin by studying these different types of angles in geometry.
The parts of an angle are:
- Vertex – Point where the arms meet
- Arms – Two straight line segments from a vertex
- Angle – If a ray is rotated about its end-point, the measure of its rotation is called angle between its initial and final position
Types of Angles
Angles can be classified into two main types:
- Based on Magnitude
- Based on Rotation
Angle Types Based on Magnitude
In maths, there are mainly 5 types of angles based on their direction. These 5 angle types are the most common ones used in geometry. These are:
- Acute Angles
- Obtuse Angles
- Right Angles
- Straight Angles
- Reflex Angles
The images below illustrate certain types of angles.
An acute angle lies between 0 degrees and 90 degrees or in other words, an acute angle is one that is less than 90 degrees. The figure below illustrates an acute angle.
An obtuse angle is the opposite of an acute angle. It is the angle which lies between 90 degrees and 180 degrees or in other words, an obtuse angle is greater than 90 degrees and less than 180 degrees. The figure below illustrates an obtuse angle.
A right angle is always equal to 90 degrees. Any angle less than 90 degrees is an acute angle whereas any angle greater than 90 degrees is an obtuse angle. The figure below illustrates a right angle or a 90-degree angle.
A straight angle is 180 degrees when measured. The figure below illustrates a straight angle or a 180-degree angle. You can see that it is just a straight line because the angle between its arms is 180 degrees.
Since this measurement is less than 90 degrees, the arms form an acute angle. But what about the angle on the other side? What is the larger angle that is complementary to the acute angle called? It is called a reflex angle. The image below illustrates a reflex angle.
Any angle that has a measure which is greater than 180 degrees but less than 360 degrees (which coincides with 0 degrees), is a reflex angle.
Angle Types Based on Rotation
Based on the direction of measurement or the direction of rotation, angles can be of two types:
- Positive Angles
- Negative Angles
Positive angles are those angles which are measured in a counterclockwise direction from the base. In most cases, positive angles are used to represent angles in geometry. From the origin, if an angle is drawn in the (+x,+y) plane, it forms a positive angle.
Negative angles are those angles which are measured in a clockwise direction from the base. From the origin, if an angle is drawn towards the (x,-y) plane, it forms a negative angle.
Complementary and Supplementary Angles
Apart from the aforementioned types, there are two more angle types which are complementary angles and supplementary angles. If the sum of two angles is more than 90°, they are supplementary angles and if the sum is less than 90°, the angles are complementary.