By definition of coterminal angles, the negative angle that is equivalent to an angle of 285° is equal to - 75° degrees. (Correct choice: D)
In this problem we must determine a negative angle coterminal to a given angle, two angles are coterminal when both have the same direction. Given that a complete revolution is done each 360°, we can derive an expression for angles coterminal to a given one:
θ' = θ + i · 360° (1)
Where i is the index of the coterminal angle.
If we know that θ = 285° and i = - 1, then the negative angle is:
θ' = 285° + (- 1) · 360°
θ' = - 75°
By definition of coterminal angles, the negative angle that is equivalent to an angle of 285° is equal to - 75° degrees. (Correct choice: D)
To learn more on coterminal angles: https://brainly.com/question/23093580
#SPJ1
