Degree Angle System

This figure illustrates the degree angle system which represents a full rotation as 360 units called degrees.
Figure 1: Degree Angle System

Degrees are a unit that measures angle. A full rotation in degrees is equal to . By convention, degrees are measured starting from the rightmost edge of the circle with the positive direction corresponding to counter-clockwise rotation.

Common Angles Measured in Degrees

Shown below are some common angles measured in degrees. These angles are common since they divide a full rotation into equal parts.

This figure illustrates the measured angle of 30 degrees.
Figure 2: 30 Degree Angle
This figure illustrates the measured angle of 45 degrees.
Figure 3: 45 Degree Angle
This figure illustrates the measured angle of 60 degrees.
Figure 4: 60 Degree Angle
This figure illustrates the measured angle of 90 degrees.
Figure 5: 90 Degree Angle

Radian Angle System

Advanced mathematics usually switches to the radian angle system as the preferred unit to measure angles[1]. As a result, calculators often offer an option to toggle between radians and degrees. Some programming languages only use radians for the trigonometric functions and so, if the user wants to use degrees, they need to convert degrees to radians[2].

References

  1. Radians Versus Degrees
    Wumbo (internal)
  2. Convert Angle from Degrees to Radians
    Wumbo (internal)