Imagine two lines that are going to intersect at a point. The point at which they intersect will create an angle. The angle is the deviation of another line from a reference. Basically, an angle is the region of the plane between two rays with a common origin. The rays are called sides and have a common origin, the vertex.

In the above image, the and are sides but in some textbooks, they are denoted by arms as well so don't get confused in terminologies, they both are the same. The point is the vertex and a vertex is a point where both lines or planes meet each other. An angle is positive if rotated in a counterclockwise direction and negative when rotated clockwise. There are different types of angles, let's take a look at them:

Types of Angles

1. Right-Angle

If the two straight lines/rays/planes (one horizontal and one vertical) meet each other, they will create a right angle. The identification of the right angle is that it will always be equal to { 90 }^{ \circ }.

2. Acute Angle

If the angle created by the rays/planes/lines is less than { 90 }^{ \circ }, that means you are dealing with an acute angle.

3. Obtuse Angle

If the angle created by the rays/planes/lines is greater than { 90 }^{ \circ }, that means the angle is an obtuse angle.

4. Straight Angle

If two straight lines/planes/rays (both either horizontal or vertical) meet each other, they will create a straight angle. A straight angle will always make { 180 }^{ \circ }.

5. Complete Angle

A complete angle is formed when two planes/rays/lines overlap each other completely hence resulting in an angle of { 360 }^{ \circ }.

6. Reflex Angle

If the angle is more than { 180 }^{ \circ } but less than { 360 }^{ \circ }, that means you are dealing with a reflex angle.

 

In addition, angles are measured in different units and each unit is very important to understand. Below are the types of units used to measure angles:

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Types of Units For Measuring Angles

1. Sexagesimal degree (°)

If the circumference of a circle is divided into 360 equal parts, the central angle corresponding to each of its 360 parts is an angle of one-degree sexagesimal, ({ 1 }^{ \circ }).

A degree has 60 minutes (') and a minute has 60 seconds ('').

2. Radian (rad)

It is the measure of an angle whose arc is a radio.

2 \pi = { 360 }^{ \circ }

\pi = { 180 }^{ \circ }

 

Convert { 30 }^{ \circ } to radian.

{ 30 }^{ \circ } \Rightarrow rad

\frac { \pi }{ { 180 }^{ \circ } } = \frac { \alpha }{ { 30 }^{ \circ } }

Cross multiply:

\frac { \pi }{ { 180 }^{ \circ } } \times { 30 }^{ \circ } = \alpha

\alpha = \frac { \pi }{ 6 } rad

 

 

Convert \frac { \pi }{ 3 } rad to degrees.

\frac { \pi }{ 3 } rad \Rightarrow \circ

\frac { \pi }{ { 180 }^{ \circ } } = \frac { \frac { \pi }{ 3 } }{ \alpha }

\frac { \frac { \pi }{ 3 } }{ \frac { \pi }{ { 180 }^{ \circ } } } = \alpha

\alpha = { 60 }^{ \circ }

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Hamza

Hi! I am Hamza and I am from Pakistan. My hobbies are reading, writing and playing chess. Currently, I am a student enrolled in the Chemical Engineering Bachelor program.