1. **Stating the problem:** There are two circles with chords and angles labeled. We need to find the hethered angle and analyze the construction needed for part d, given that 0 is the center of each circle. 2. **Understanding the problem:** The problem involves a circle geometry setting with chords and angles inscribed or central. 3. **Key properties:** - An inscribed angle subtending the same arc as a central angle is half the central angle. - Angles subtended by the same chord or arc are equal. 4. **Analysis of top circle:** - Given angles labeled are 4, 2, 2, 9, and 5. - If 0 is center and some angles are central, we can find related inscribed angles by halving central angles. 5. **Analysis of bottom circle:** - Angles 4, 8, 3, 9, 5, 4, 3, and 2 are labeled. - Using the intersecting chords theorem, angles inside the circle formed by chords equal half the sum of arcs intercepted. 6. **Finding the hethered angle (likely meaning 'interior angle related to chords'):** - Use formula for angle between chord intersection: $$ \text{Angle} = \frac{1}{2}(\text{arc}_1 + \text{arc}_2) $$ - Identify arcs from given angles. 7. **Construction needed for part d:** - Identify center 0 of circle. - Draw radii to endpoints of chords. - Construct arcs from chord endpoints and measure relevant arcs. - Use inscribed angle theorem and chord properties to find target angles. 8. **Summary:** The hethered angle is calculated from the arcs intercepted by the chords involved, using the formula above. Construction involves drawing radii, arcs, and applying circle theorems on chords and angles. **Final answer:** The hethered angle is equal to half the sum of the intercepted arcs on the circle by the chords forming that angle, and the construction requires the center 0, radii, and chord arcs to calculate this angle precisely.