Final answer:
The closest positive coterminal angle to 200° is 560° and the closest negative coterminal angle is -160°.
Step-by-step explanation:
To find the closest positive angle and the closest negative angle that are coterminal to 200°, we'll look for angles that differ from 200° by multiples of 360°. Since 360° is the angle for one complete revolution, any angle ± 360° will be coterminal with the original angle.
The closest positive coterminal angle can be found by adding 360° to the given angle if it's negative, or subtracting 360° if the angle exceeds 360°.
In the case of 200°, the closest positive coterminal angle would be 200° + 360° = 560°. To find the closest negative coterminal angle, we subtract 360° from 200°, but since the result (200° - 360° = -160°) is negative, it's already the closest negative coterminal angle.
The closest positive coterminal angle to 200° is 560° and the closest negative coterminal angle to 200° is -160°.