Answered

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Which negative angle is equivalent to [tex]$285^{\circ}$[/tex]?

A. [tex]$-85^{\circ}$[/tex]
B. [tex][tex]$-95^{\circ}$[/tex][/tex]
C. [tex]$-75^{\circ}$[/tex]
D. [tex]$-65^{\circ}$[/tex]

Sagot :

GinnyAnswer
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.
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