The expression 180 degrees - x is used to determine the reference angle for angle x = 150 degrees.
In trigonometry, There are 4 quadrants in between [tex]0^\circ[/tex] to [tex]360^\circ[/tex].
These quadrants can be expressed as,
Quadrant 1 = [tex]0^\circ[/tex] to [tex]90^\circ[/tex]
Quadrant 2 = [tex]90^\circ[/tex] to [tex]180^\circ[/tex]
Quadrant 3 = [tex]180^\circ[/tex] to [tex]270^\circ[/tex]
Quadrant 4 = [tex]270^\circ[/tex] to [tex]360^\circ[/tex]
Any angle lies between these quadrants is called quadrant angle.
The reference angle for any quadrant can be calculated as shown in the attachment.
Given that angle [tex]x=150^\circ[/tex]. It means that angle [tex]x[/tex] lies in the quadrant 2.
So the reference angle can be calculated as,
Reference angle = [tex]180^\circ - \angle x[/tex]
Reference angle = [tex]180^\circ -150^\circ[/tex]
Reference angle = [tex]30^\circ[/tex]
The expression 180 degrees - x is used to determine the reference angle for angle x = 150 degrees.
For more details about the reference angle, follow the link given below.
https://brainly.com/question/7099725
