Math Geometry Angles in a Circle Worksheet

Geometry CP Angles in a Circle Worksheet Name_____________________________________________ Find the measures of the arcs or angles as indicted. Circle the types of angles you see in each diagram. Use these to determine which rules to use. The center is emphasized in each circle with a bold point. Some of these are combination problems so you might have to circle more than one! 1. m∠A Where is the vertex located? Center Circle Inside Outside T-T Center m∠A = ___________ 4. 5. Where is the vertex located? Circle Inside Outside T-T Outside T-T m∠1 Center 6. Circle Inside Circle m∠1 = ___________ Inside Outside T-T T-T Circle Outside T-T Outside T-T Outside T-T m∠1 Center 9. Center Inside Circle Inside m∠1 = ___________ Where is the vertex located? Outside Circle Where is the vertex located? 8. Where is the vertex located? Center m∠B = ___________ = _____ m∠1 = ___________ m∠1 Center Inside m∠B Where is the vertex located? Where is the vertex located? m∠1 = ___________ 7. Circle = _____ AND m∠1 Center 3. 2. Where is the vertex located? Inside = ___________ x Where is the vertex located? Outside T-T Center Circle x = ___________ Inside 10. m∠D and m∠C 11. Where is the vertex located? Center Circle m∠D = _______ 13. Inside AND Outside T-T m∠C = _______ Where is the vertex located? Inside Outside T-T m∠2 m ARC1 = ______ Outside T-T x Center Inside 15. Circle Inside AND T-T Outside T-T m∠2 = ______ x = ___________ Inside AND Outside T-T m∠2 = _______ m∠C Center 18. Circle Circle Circle Inside Outside T-T m∠C = ____________ x Center m∠2 Where is the vertex located? Where is the vertex located? Outside Center m∠1 = _______ m∠A = ___________ 17. Where is the vertex located? Circle Inside x = ___________ m ARC 1 and Center Circle m∠1 and Where is the vertex located? Where is the vertex located? m∠1 = ___________ 16. Center 14. Circle 12. Where is the vertex located? m∠1 Center m∠A Inside m ARC 1 and m∠2 Where is the vertex located? Outside T-T Center Circle m ARC1 = ______ Inside AND Outside T-T m∠2 = ______ 19. m∠1 20. Where is the vertex located? Center Circle Inside Outside T-T Center 23. Where is the vertex located? Circle Circle Inside Inside Outside T-T T-T x Center 24. Circle x and y Circle Inside Outside T-T Inside Outside T-T x Where is the vertex located? Outside T-T x = ___________ x = ___________ Find the value of each variable using a combination of rules. 25. Center m∠1 = ____________ Where is the vertex located? Outside m∠1 Where is the vertex located? m∠1 = ___________ x Center 21. Where is the vertex located? m∠1 = ___________ 22. m∠1 Center Circle Inside x = ____________ 26. x, y, w, and z VERTEX ON Circle AND QUADRILATERAL INSCRIBED IN A CIRCLE VERTEX ON Circle AND QUADRILATERAL INSCRIBED IN A CIRCLE The OPPOSITE ANGLES are ________________________. The OPPOSITE ANGLES are ________________________. x = ___________ AND y = ___________ x = _______ y = _______ w = _______ z = _______ NOW YOU ARE READY FOR COMBO PROBLEMS! Use Circle O to find the following angles. 27. m∠1 = ___________ Where is the vertex located? Center Circle Inside Outside T-T 28. m∠2 =___________ Where is the vertex located? Center Circle Inside Outside T-T 29. m∠3 = ___________ Where is the vertex located? Center Circle Inside Outside T-T 30. m∠4 = ___________ Where is the vertex located? Center Circle Inside Outside T-T 31. m∠5 = ___________ Where is the vertex located? Center Circle Inside Outside T-T 32. m∠6 = ___________ Where is the vertex located? Center Circle Inside Outside T-T Use Circle O to find the following angles AND arcs. Which rule did you use? 33. m∠A = ___________ Which rule did you use? 34. m∠ACO =___________ Which rule did you use? 35. m∠COE = ___________ Which rule did you use? 36. m Arc AC = ___________ Which rule did you use? 37. m Arc CE = ___________ Which rule did you use? 38. m Arc AEC = ___________