1. The problem asks to find the matching counterclockwise angle for given clockwise angles 175° and 285°. 2. Important rule: A full circle is 360°. Clockwise and counterclockwise angles are measured in opposite directions. 3. To find the counterclockwise angle matching a clockwise angle $\theta$, use the formula: $$\text{Counterclockwise angle} = 360^\circ - \theta$$ 4. For part (a), clockwise angle is 175°: $$360^\circ - 175^\circ = 185^\circ$$ So, the matching counterclockwise angle is 185°. 5. For part (b), clockwise angle is 285°: $$360^\circ - 285^\circ = 75^\circ$$ So, the matching counterclockwise angle is 75°. 6. We know this because the sum of clockwise and counterclockwise angles around a point is always 360°, representing a full rotation. Final answers: - a) 185° - b) 75°