Degrees

Definition

The unit of an angle that expresses one in three hundred and sixtieth of the circumference of a circle is called degree.

Introduction

Degree is a unit of measuring angles in sexagesimal system. It is not an S.I unit but it is accepted by the S.I standards. So, we must know what the degree is, while studying the angles in geometry.

The locus of a point forms a circle, whereas a line segment is formed when its center is connected by a straight line with any point on the circumference, and its length is the radius of circle. An equilateral triangle can be constructed by connecting two radii and a chord having the equal length of radius.

Now, let’s consider an arc that connects the vertices of triangle. Divide the arc into sixty equal parts from the center. Then, an angle is formed between every two lines and the angle of each sector is called degree.

1. The horizontal line is parallel to the surface of earth. It can be considered as a reference line of measuring angles and it does not make any angle with the surface of earth geometrically. So, its angle is zero degrees.
2. The first line makes an angle with the reference line. So, its angle is one degree.
3. Similarly, each line makes an angle with the reference line and the angle made by every line is successor to the previous line. In this case, the angle made by the last line with reference line is sixty degrees.

In the same way, the circumference of a circle can be divided into three hundred sixty equal parts. You can observe it in the below image.

There are $90$ line-segments between every two vertical lines.

1. The angle of first quadrant is Ninety degrees.
2. The angle of second quadrant is One hundred eighty degrees.
3. The angle of third quadrant is Two hundred seventy degrees.
4. The angle of fourth quadrant is Three hundred sixty degrees.

Notation

The angles are written in words but it is tough to write them every time; whereas, writing the angles in mathematical form is easy. So, let’s learn how to represent the angles mathematically in sexagesimal system.

In sexagesimal system, the symbol $^\circ$ is used to denote degree in mathematics. If measure of an angle is Sixty degrees, then it is written as $60^\circ$ in mathematics.

1. Ninety degrees is written as $90^\circ$.
2. One hundred eighty degrees is written as $180^\circ$.
3. Two hundred seventy degrees is written as $270^\circ$.
4. Three hundred sixty degrees is written as $360^\circ$.

In this way, any angle can be written easily in mathematics as per the sexagesimal system.

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