Final answer:
The closest positive angle coterminal to 102° is 462° and the closest negative angle coterminal is -258°. Angles are coterminal if they have the same terminal side, differing by full rotations (360°).
Step-by-step explanation:
The question asks us to find the closest positive angle and the closest negative angle that is coterminal to 102°. Coterminal angles are angles that share the same terminal side but may differ by any number of full rotations. One full rotation in the standard unit of angles is 360°.
To find the closest positive coterminal angle to 102°, we can add 360° to it:
Positive coterminal angle = 102° + 360° = 462°
To find the closest negative coterminal angle to 102°, we can subtract 360° from it:
Negative coterminal angle = 102° - 360° = -258°
Therefore, the closest positive angle coterminal to 102° is 462° and the closest negative angle coterminal to 102° is -258°.