Final answer:
The closest positive coterminal angle to 80° is 440°, and the closest negative coterminal angle to 80° is -280°.
Step-by-step explanation:
To find the closest positive angle and the closest negative angle that is coterminal to 80°, we utilize the fact that coterminal angles differ by 360° multiples. Since angles are generally measured in degrees, adding or subtracting 360° to the original angle gives us coterminal angles.
The closest positive angle coterminal with 80° is simply 80° + 360°, which equals 440°.
The closest negative angle coterminal with 80° is 80° - 360°, which equals -280°.
These calculations provide the simplest coterminal angles, one positive and one negative, to the given angle of 80°.
Therefore, the closest positive angle that is coterminal to 80° is 80° and the closest negative angle is -280°.