Centesimal System of Angle Measurement

According to geometry, if the adjacent angles formed by a straight line standing on another line are equal, then each of these angles is a right angle. The unit of measure of an angle is degree. The symbol representing it ∠. The right angle is the base for defining the measurement system of angles. 

Today, we will learn about the Centesimal system of angle measurement. In this system, Grade or Gradian is the unit of measure of an angle. According to the centesimal system, a right angle is split into 100 equal parts, and each component is called a grade. We will also cover some examples for a better understanding. 

Different Angle Measurement Systems

The three different systems of angle measurement are:

• Sexagesimal System of Angle Measurement or The English system:

In the Sexagesimal System, the right angle is split into 90 equal parts. Each part is known as a degree.

• Centesimal System of Angle Measurement or The French system:

In the Centesimal System, the right angle is split into 100 equal parts. Each part is known as a grade.

• Circular system of angle measurement:

In a circular system, Radian is used to measure the angle. The arc of length equals radius, subtending an angle of 1 Radian at the circle’s centre.

Circular System

Radian is a unit of measure of an angle in the circular system. The system found its place in higher mathematics. 

Suppose an arc whose length equals the radius subtends an angle at the circle’s centre. Then this angle is known as radian. 1c denotes it.

Sexagesimal System of Angle Measurement

The Sexagesimal system, also known as the English system, is the most preferred angle measurement system. Degrees, Minutes and Seconds are the units of measure in the sexagesimal system. In this system, the right angle is split into 90 equally divided parts. Each part is called a degree. (1°). 

Furthermore, one degree is split into 60 equally divided parts. Each part is known as the sexagesimal minute (1’). Every single minute is split into 60 equally divided parts, known as the sexagesimal second (1”).

This system is prevalent and widely used in practical applications of Trigonometry. 

Centesimal System of Angle Measurement

Originally, metric units planned to replace existing time and angle units. But the French revolutionaries introduced the decimal division of the day and angles. 

In the Centesimal system of angle measurement, the right angle is split into 100 equally divided parts known as Grades. Each grade is split in 100 minutes and every single minute in 100 seconds. 

1 right angle = 100g (100 grades)

1 grade = 100” (100 minutes)

1 minute = 100’ (100 seconds)

This measurement system is more convenient to use than the sexagesimal system. 

Minutes and seconds are different in the Sexagesimal centesimal system of angle measurement. 

Right Angle = 90 × 60 = 5400 sexagesimal minutes = (5400)’ 

and Right Angle = 100 × 100 = 10000 Centesimal minutes = (10000)’

The relation between the sexagesimal system of angle measurement and centesimal system of angle measurement is as follows

Centesimal System of Angle Measurement Examples

Drawbacks of centesimal system of angle measurement

In the centesimal system, a right angle is 100 grades, each grade is 100 minutes and every single minute is 100 seconds. This makes it difficult for ordinary users to understand as they have been using the sexagesimal system for a long time. Also, the degrees are identical in size in the sexagesimal measurement system. 

Also, if an angle is not an integral number, it is first reduced to a fraction of degree before being converted to the centesimal angle measurement system.

Thus, due to the above drawbacks and based on the complexity of the centesimal system of angle measurement, it is clear that using the system daily is difficult.

Conclusion

This article covers the difference between the three main systems of angle measurement. From this article, one can obtain a relation between the sexagesimal system of angle measurement and the centesimal system of angle measurement. It also indicates the benefits of both systems of angle measurement.

The centesimal system of angle measurement did not receive much recognition because of its complexity. Also, the sexagesimal angle measurement system had already penetrated the mathematics society so profoundly, that the mathematicians could not understand and accept the centesimal system.