https://file.aiquickdraw.com/mathbot/file/1730811848479rmcm3n7u.jpg

Let's go through each question based on the diagrams and provided values.

### For the first circle (with diameter \( PQ \)):

1. **10. \( m\angle QOR \)**: 
   - Since \( PQ \) is the diameter, angle \( QOR \) forms a central angle of \( 75^\circ \) as marked in the figure.
   - **Answer**: \( m\angle QOR = 75^\circ \).

2. **11. \( m\overarc{PR} \)**:
   - Arc \( PR \) corresponds to the central angle \( QOR = 75^\circ \).
   - **Answer**: \( m\overarc{PR} = 75^\circ \).

3. **12. \( m\overarc{QR} \)**:
   - Since \( PQ \) is the diameter, the circle is divided into two semicircles, meaning \( m\overarc{QR} \) is the remaining arc.
   - To find \( m\overarc{QR} \), subtract \( 75^\circ \) from \( 180^\circ \).
   - **Answer**: \( m\overarc{QR} = 180^\circ - 75^\circ = 105^\circ \).

4. **13. \( m\overarc{PSQ} \)**:
   - Arc \( PSQ \) represents the entire circle minus arc \( PR \).
   - **Answer**: \( m\overarc{PSQ} = 360^\circ - 75^\circ = 285^\circ \).

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### For the second circle (with diameter \( FD \)):

1. **14. \( m\angle COF \)**:
   - \( COF \) forms a central angle of \( 45^\circ \) as marked in the figure.
   - **Answer**: \( m\angle COF = 45^\circ \).

2. **15. \( m\overarc{FC} \)**:
   - Arc \( FC \) corresponds to the central angle \( COF = 45^\circ \).
   - **Answer**: \( m\overarc{FC} = 45^\circ \).

3. **16. \( m\overarc{CDE} \)**:
   - To find \( m\overarc{CDE} \), add the central angles corresponding to arcs \( CD \) and \( DE \): \( 118^\circ + 75^\circ = 193^\circ \).
   - **Answer**: \( m\overarc{CDE} = 193^\circ \).

4. **17. \( m\overarc{CFE} \)**:
   - Arc \( CFE \) represents the entire circle minus arc \( FD \).
   - Since \( FD \) is a diameter, it subtends a semicircle of \( 180^\circ \).
   - **Answer**: \( m\overarc{CFE} = 360^\circ - 180^\circ = 180^\circ \).

Would you like further explanations on any of these steps?

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### Additional Related Questions

1. How can we calculate the measure of an arc given its central angle?
2. Why does a diameter divide a circle into two equal arcs?
3. How would you find the measure of a minor arc versus a major arc?
4. What properties of a circle help in calculating angle measures?
5. How do central angles relate to the arcs they intercept?

### Tip
Remember, a central angle in a circle always equals the measure of the arc it intercepts.

In the given figure, PQ and FD are diameters of circles O. Find the indicated measures for angles and arcs.

Explore how to find measures of angles and arcs in circles with diameters as given in the problem. This involves understanding central angles, arcs, and the relationship between them, using concepts from geometry. Suitable for students in Grades 8-10.

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