Sorry, no online dictionaries contain the exact phrase degrees of arc.
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Reverse dictionary results:
1. octant
 2. angular
3. quadrant
4. kriesel
5. omega
6. degree
7. sextant
8. coordinate
9. declination
10. supplement
 11. carbon
12. radian
13. third
14. bow
15. longitude
16. praseodymium
17. samarium
18. xenon
19. between
20. direction
 21. dwell
22. dynamics
23. extent
24. far
25. fsr
26. graduate
27. inch
28. oblique
29. order
30. point
 31. protractor
32. sheer
33. slip
34. time
35. uranus
36. accent
37. amplitude
38. chord
39. compass
40. curvature

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You can look up the words in the phrase individually using these links:   degrees ?   of ?   arc ?
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