To find the reference angle of a given angle, we need to consider its location on the unit circle and determine how far it is from the nearest x-axis.
A [tex]$240^{\circ}$[/tex] angle is in the third quadrant of the unit circle since it is greater than [tex]$180^{\circ}$[/tex] but less than [tex]$270^{\circ}$[/tex].
The reference angle is the smallest angle formed by the terminal side of the given angle and the x-axis. In the third quadrant, the reference angle can be found by subtracting the given angle from [tex]$360^{\circ}$[/tex]:
[tex]\[ \text{Reference angle} = 360^{\circ} - 240^{\circ} \][/tex]
[tex]\[ \text{Reference angle} = 120^{\circ} \][/tex]
Thus, the reference angle for a [tex]$240^{\circ}$[/tex] angle is [tex]\( \boxed{120^{\circ}} \)[/tex].
