How Do You Find the Reference Angle of Another Angle?
Answer – To find the reference angle B of another angle A, recognize the terminal side of A, identify the quadrant it ends in, and apply the relevant formula from below:
| Quadrant | Angle A | Reference Angle B |
| I | 0° to 90° | Equal to A |
| II | 90° to 180° | 180 – A |
| III | 180° to 270° | A – 180 |
| IV | 270° to 360° | 360 – A |
Explanation:
A reference angle is one formed by the terminal side of a given angle and the x-axis. It is always acute.
The image below illustrates the reference angle B for another angle A.
Considering the x-axis is a 180° angle and angle A terminates in Quadrant II, angle B can be found by subtracting the absolute value of angle A from 180°.
So if A = 120°, then B = 180° – 120° = 60°
Depending on the quadrant of the angle A, the appropriate formula needs to be used to calculate the corresponding reference angle.
