Angles: An Introduction
Angle Meaning
The amount of rotation about the point of intersection of two planes (or lines) which is required to bring one in correspondence with the other is called an Angle. There are many different types of angles which we will study in this article.
Angle Definition
In the angle ∠ABC(Like given above), it is generally represented by Greek letters such as θ, α, β etc.
It can also be represented by three letters of the shape that define the angle, with the middle letter being where the angle actually is (i.e.its vertex).
Eg. ∠ABC, where B is the given angle.
Angle measurement terms are – degree °, radians or gradians.
Types of Angles
- Acute Angle – 0° to 90°, both exclusive.
- Obtuse Angle – 90° to 180°, both exclusive.
- Right Angle – Exactly 90°.
- Straight Angle – Exactly 180°.
- Reflex Angle – 180° to 360°, both exclusive.
- Full Rotation – Exactly 360°
Type of angles |
Description |
Acute Angle |
An Angle less than 90° |
Obtuse Angle |
An Angle greater than 90° |
Right Angle |
An Angle equal to 90°. |
Straight Angle |
An Angle which is exactly 180°. |
Reflex Angle |
An Angle greater than 180° |
Positive & Negative Angles
- Positive Angle- An Angle measured in Anti-Clockwise direction is Positive Angle.
- Negative Angle- An angle measured in Clockwise direction is Negative Angle.
Parts of Angles
- Vertex- The corner points of an angle is known as Vertex. It is the point where two rays meet.
- Initial Side - It is also known as the reference line. All the measurements are done taking this line as the reference.
- Terminal Side- It is the side (or ray) up to which the angle measurement is done.
Angle Measurement
To measure everything in this world, we need a unit in a similar angle measurement requires three units of measurement :
Degree of an Angle
It is represented by ° (read as a degree). It most likely comes from Babylonians, who used a base 60 (Sexagesimal) number system. In their calendar, there was a total of 360 days. Hence, they adopted a full angle to be 360°. First, they tried to divide a full angle into angles using the angle of an equilateral triangle. Later, following their number system (base 60), they divided 60° by 60 and defined that as 1°. Sometimes, it is also referred to as arc degree or arc-degree which means the degree of an arc.
An angle is said to be equal to 1° if the rotation from the initial to the terminal side is equal to 1/360 of the full rotation.
A degree is further divided into minutes and seconds. 1′ (1 minute) is defined as one-sixtieth of a degree and 1” (1 second) is defined as one-sixtieth of a minute. Thus,
1°= 1′
1′ = 1”
Angle Measurement in Degrees
Radian of an Angle
This is the SI unit of angle. Radian is mostly used in Calculus. All the formula for derivatives and integrals hold true only when angles are measured in terms of a radian. It is denoted by ‘rad’.
The length of the arc of a unit circle is numerically equal to the measurement in radian of the angle that it subtends.
In a complete circle, there are 2π radians.
360 = 22π; radian
Therefore, 1 radian = 180°/π
Gradian of an Angle
This unit is least used in Maths. It is also called a gon or a grade.
An angle is equal to 1 gradian if the rotation from the initial to terminal side is 1/400 of the full rotation. Hence, the full angle is equal to 400 gradians.
It is denoted by ‘grad’.
Figure 3 shows the example of angles in gradian.
Figure 3: Angle Measurement in Gradian.