1. The problem involves understanding angles on a Ferris wheel, their positions, and coterminal angles. 2. The Ferris wheel rotates counterclockwise, starting at 0° on the rightmost point. 3. Reference angles indicate the seat's position in different quadrants or axes: - 75° in Quadrant I (upper-right) - 45° in Quadrant IV (below center, right side) - 60° in Quadrant I (upper-right after one full turn) - 90° on the negative y-axis (bottom) - 20° in Quadrant III (lower-left) 4. Coterminal angles are angles that differ by full rotations of 360° but point to the same position: - For example, 75° has positive coterminal 435° ($75° + 360°$) and negative coterminal -285° ($75° - 360°$). 5. The table of coterminal angles: Original Angle | Positive Coterminal | Negative Coterminal 75° | 435° | -285° -45° | 315° | -405° 420° | 780° | -300° -810° | 270° | -450° 200° | 560° | -160° 6. To find coterminal angles, add or subtract multiples of 360°: $$\text{Coterminal angle} = \text{Original angle} \pm 360° \times k, \quad k \in \mathbb{Z}$$ 7. This explains how the Ferris wheel seat returns to the same position after full rotations. Final understanding: Angles repeat every 360°, and coterminal angles represent the same seat position on the Ferris wheel after multiple rotations.