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Understanding Measures of Central Angles and Arc Lengths in Circle Geometry

This guide explores how to find the measures of central angles and arcs in circle geometry through various examples. It covers key concepts, including how to substitute values and simplify equations to find unknown variables such as x. With step-by-step examples, we apply the Arc Addition Postulate and learn to calculate arc lengths using appropriate formulas. Additionally, the guide emphasizes the importance of understanding the relationship between the sum of arcs and circle properties. Perfect for students looking to grasp circle geometry fundamentals.

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Understanding Measures of Central Angles and Arc Lengths in Circle Geometry

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Presentation Transcript

  1. Concept

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

  3. 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

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

  5. Concept

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

  7. Classify Arcs and Find Arc Measures Example 2

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

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

  10. Concept

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

  12. Find Arc Measures in Circle Graphs Example 3

  13. Answer: Find Arc Measures in Circle Graphs Sum of arcs in a circle is 360. Substitution Simplify. Simplify. Example 3

  14. Concept

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

  16. Answer: Use Arc Addition to Find Measures of Arcs Arc Addition Postulate = 58 + 32 Substitution = 90 Example 4

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

  18. Answer: Use Arc Addition to Find Measures of Arcs Arc Addition Postulate = mIMJ + mJMK Substitution = 90 + 58 = 148 Example 4

  19. Concept

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

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

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

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