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Dive into the fundamentals of central angles and arc measures with this comprehensive lesson. Learn how to classify arcs, find their measures, and explore real-world applications. We cover the concepts of minor arcs, major arcs, semicircles, and congruence while practicing with examples. Essential postulates, like the Arc Addition Postulate, will be explained, followed by exercises to reinforce your understanding. Master the skills to calculate arc lengths and better understand circle graphs. Prepare for quizzes with five-minute checks and interactive questions.

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 10–1) Then/Now New Vocabulary Key Concept: Sum of Central Angles Example 1: Find Measures of Central Angles Key Concept: Arcs and Arc Measure Example 2: Classify Arcs and Find Arc Measures Theorem 10.1 Example 3: Real-World Example: Find Arc Measures in Circle Graphs Postulate 10.1: Arc Addition Postulate Example 4: Use Arc Addition to Find Measures of Arcs Key Concept: Arc Length Example 5: Find Arc Length Lesson Menu

  3. A B C D Name a radius. A. B. C. D. 5-Minute Check 1

  4. A B C D Name a chord. ___ A.LF B.MF C.OM D.NF ___ ___ ___ 5-Minute Check 2

  5. A B C D Name a diameter. ____ A.OM B.OL C.NF D.MF ___ ___ ____ 5-Minute Check 3

  6. A B C D Refer to the figure. Find BC. A. 2 B. 3 C. 4 D. 5 5-Minute Check 4

  7. A B C D Refer to the figure. Find DE. A. 9 B. 11 C. 13 D. 15 5-Minute Check 5

  8. A B C D Find the length of the radius of the circle. A. 6.5 in. B. 10.9 in. C. 13 in. D. 17 in. 5-Minute Check 6

  9. You measured angles and identified congruent angles. (Lesson 1–4) • Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. • Find arc lengths. Then/Now

  10. central angle • arc length • arc • minor arc • major arc • semicircle • congruent arcs • adjacent arcs Vocabulary

  11. Concept

  12. Find Measures of Central Angles Find the value of x. Example 1

  13. The sum of the measures of Find Measures of Central Angles Substitution Simplify. Add 2 to each side. Divide each side by 26. Answer:x = 7 Example 1

  14. A B C D Find the value of x. A. 9 B. 10 C. 11 D. 65 Example 1

  15. Concept

  16. Answer: Classify Arcs and Find Arc Measures Example 2

  17. Classify Arcs and Find Arc Measures Example 2

  18. Answer: Classify Arcs and Find Arc Measures Example 2

  19. Answer: Classify Arcs and Find Arc Measures Example 2

  20. A B C D A. B. C. D. Example 2

  21. A B C D A. B. C. D. Example 2

  22. A B C D A. B. C. D. Example 2

  23. Concept

  24. Answer: Find Arc Measures in Circle Graphs mLPK = 0.21(360) Find 21% of 360. = 75.6 Simplify. Example 3

  25. Find Arc Measures in Circle Graphs Example 3

  26. Answer: Find Arc Measures in Circle Graphs Sum of arc in circle is 360. Substitution Simplify. Simplify. Example 3

  27. A B C D A. 124.3 B. 140.4 C. 155.6 D. 165.9 Example 3

  28. A B C D A. 273.6 B. 240.5 C. 215.7 D. 201.4 Example 3

  29. Concept

  30. . Use Arc Addition to Find Measures of Arcs Example 4

  31. Answer: Use Arc Addition to Find Measures of Arcs Arc Addition Postulate = mLH + mHI Substitution = 58 + 32 = 90 Example 4

  32. Use Arc Addition to Find Measures of Arcs Example 4

  33. Answer: Use Arc Addition to Find Measures of Arcs Arc Addition Postulate = mIJ + mJK Substitution = 90 + 58 = 148 Example 4

  34. A B C D A. 38 B. 52 C. 90 D. 180 Example 4

  35. A B C D A. 52 B. 90 C. 142 D. 180 Example 4

  36. Concept

  37. cm Use a calculator. Answer: Find Arc Length Arc Length Equation Substitution Example 5

  38. Answer: Find Arc Length Arc Length Equation Substitution Use a calculator. Example 5

  39. Answer: Find Arc Length Arc Length Equation Substitution Use a calculator. Example 5

  40. A B C D A. 3.56 cm B. 3.77 cm C. 3.98 cm D. 4.21 cm Example 5

  41. A B C D A. 36.56 cm B. 37.79 cm C. 38.61 cm D. 40.21 cm Example 5

  42. A B C D A. 32.99 cm B. 33.59 cm C. 33.89 cm D. 34.61 cm Example 5

  43. End of the Lesson

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