To determine the negative angle equivalent to [tex]\( 285^\circ \)[/tex], we need to convert the positive angle to its corresponding negative angle within a 360-degree rotation.
Here's the step-by-step solution:
1. Start with the given positive angle: [tex]\( 285^\circ \)[/tex].
2. Subtract [tex]\( 360^\circ \)[/tex] from the given angle to find its corresponding negative angle:
[tex]\[
285^\circ - 360^\circ = -75^\circ
\][/tex]
Thus, the negative angle that is equivalent to [tex]\( 285^\circ \)[/tex] is [tex]\(-75^\circ\)[/tex].
Therefore, the correct answer is [tex]\( \boxed{-75^\circ} \)[/tex], which corresponds to option C.
