Final answer:
The closest positive coterminal angle to 265° is 625°, and the closest negative coterminal angle is -95°. This is found by adding or subtracting 360° from the given angle.
Step-by-step explanation:
The student is asking how to find the closest positive angle and the closest negative angle that are coterminal to 265°. To find coterminal angles, we have to add or subtract multiples of 360° from the given angle.
To find the closest positive coterminal angle, we can subtract 360° from 265° (since 265° is less than 360°, there is no need to add 360° to find a positive coterminal angle closer than itself).
265° - 360° = -95°
The closest negative coterminal angle would be -95°, as it's less than 360° away from the initial angle.
To find the closest negative coterminal angle, we simply add 360° to the initial angle:
265° + 360° = 625°
Therefore, the answer in 200 words, the closest positive coterminal angle to 265° is 625° and the closest negative coterminal angle is -95°.