In geometry, you will various math concepts like Angles, Lines, Shapes, Area and Perimeter, etc. Today, we will discuss completely the concept named Angles and its types. Based on measurements, there are various types of angles. Usually, an angle is measured in degrees and it is one of the core concepts of geometry in Maths. Are you excited to learn deeply about the topic called Angle? Then, refer to the below modules thoroughly and know what is an angle, what are the Types of Angles, definitions, figures, and some solved examples.
What is an Angle?
An Angle is a geometrical shape formed when two rays join with a common end-point. “side and vertex’ are the two components of an angle. Angles are classified based on their measures.
Parts of Angle
- Vertex – Point where the arms meet.
- Arms – Two straight line segments form a vertex.
- Angle – When a ray turn about its endpoint, the measure of its rotation between its initial and final position is called Angle.
If these two ray joins in various fashions to form a various type of angles in maths. Let’s, start learning what are the different types of angles and their definitions and figures.
Classification of Angles
In nature, there are several types of angles that exist. Each and every angle of them hold great value in our everyday living standards.
Basically, Angles are classified on the basis of:
- Magnitude
- Rotation
Types of Angles Based on Magnitude
In maths, mainly, there are 6 types of angles on the basis of direction. And also, all these six angle types are commonly used in geometry. The names of different angles types are as follows:
- Acute Angle
- Obtuse Angle
- Right Angle
- Straight Angle
- Reflex Angle
- Complete Angle
The below image illustrates specific types of angles based on magnitude:
1. Acute Angle:
An acute angle is an angle that lies between 0 degrees to 90 degrees. In other words, an angle is less than 90° is called an acute angle.
Illustration:
∠XYZ is greater than 0° but less than 90° so, this is an acute angle type.
2. Obtuse Angle:
Opposite of the Acute angle is called Obtuse Angle. In other words, the angle that lies between 90 degrees and 180 degrees is known as the obtuse angle.
Illustration:
3. Right Angle:
An angle that measures at exactly 90 degrees is called a right angle. Basically, it forms when two lines are perpendicular to each other. See the below-illustrated figure of a right angle.
4. Straight Angle:
An angle that measures 180° is known as Straight angle. The following figure illustrated the straight angle.
5. Reflex Angle:
The angle that lies between 180 degrees and 360 degrees is called a reflex angle. If you want to calculate the reflex angle then you must require an acute angle. The below figure illustrates the reflex angle.
6. Complete Angle:
An angle measured 360 degrees is called a Complete Angle. 1 Revolution is equal to 360° and the illustration of the complete angle is as shown in the below figure:
Solved Examples on Types of Angles
1. The sum of three angles is (x+6), (x -4), and (x + 8) forms a right angle. Find the value of x.
Solution:
⇒ (x+6) + (x-4) + (x+8) = 90
⇒ 3x + 10 = 90
⇒ 3x = 80
x = 26
Therefore, the value of x is 26 degrees.
2. A certain angle is such that, two times the sum of its size and 70° is 90°. What is the name of this angle?
Solution:
The angle be x°
⇒ 2(x + 70°) = 90°
⇒ 2x + 140° = 90°
⇒ 2x = 50°
x = 25°
The angle is 25°
Since 25° is less than 90°, so the type of the angle is an Acute angle.