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10-4

10-4. Angle Relationships in Circles. Warm Up. Lesson Presentation. Lesson Quiz. Holt Geometry. 10.4 Other Angles Relationships in Circles. chords: AE , CD secant: AE tangent: AB. Warm Up 1. Identify each line or segment that intersects  F . Find each measure. 2. m  NMP

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10-4

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  1. 10-4 Angle Relationships in Circles Warm Up Lesson Presentation Lesson Quiz Holt Geometry

  2. 10.4 Other Angles Relationships in Circles chords:AE,CD secant: AE tangent: AB Warm Up 1.Identify each line or segment that intersects F. Find each measure. 2. mNMP 3. mNLP 110° 55°

  3. 10.4 Other Angles Relationships in Circles Objectives Find the measures of angles formed by lines that intersect circles. Use angle measures to solve problems.

  4. 10.4 Other Angles Relationships in Circles

  5. 10.4 Other Angles Relationships in Circles Example 1A: Using Tangent-Secant and Tangent-Chord Angles Find each measure. mEFH = 65°

  6. 10.4 Other Angles Relationships in Circles Example 1B: Using Tangent-Secant and Tangent-Chord Angles Find each measure.

  7. 10.4 Other Angles Relationships in Circles Check It Out! Example 1a Find each measure. mSTU = 83

  8. 10.4 Other Angles Relationships in Circles Check It Out! Example 1b Find each measure.

  9. 10.4 Other Angles Relationships in Circles

  10. 10.4 Other Angles Relationships in Circles Example 2: Finding Angle Measures Inside a Circle Find each measure. mAEB = 126

  11. 10.4 Other Angles Relationships in Circles Check It Out! Example 2a Find each angle measure. mABD

  12. 10.4 Other Angles Relationships in Circles Check It Out! Example 2b Find each angle measure. mRNM mRNM = 180° – MNQ mRNM = 180° – 158° = 22°

  13. 10.4 Other Angles Relationships in Circles

  14. 10.4 Other Angles Relationships in Circles Example 3: Finding Measures Using Tangents and Secants Find the value of x. = 40 = 63

  15. 10.4 Other Angles Relationships in Circles Check It Out! Example 3 Find the value of x. 50° = 83° – x x= 33°

  16. 10.4 Other Angles Relationships in Circles In the company logo shown, = 108°, and = 12°. What is mFKH? Example 4: Design Application

  17. 10.4 Other Angles Relationships in Circles Two of the six muscles that control eye movement are attached to the eyeball and intersect behind the eye. If mAEB = 225, what is mACB? Check It Out! Example 4

  18. 10.4 Other Angles Relationships in Circles

  19. 10.4 Other Angles Relationships in Circles Find Step 1 Find U V Substitute 180 – 113 for mXVY and 68 for mWZ Example 5: Finding Arc Measures If a tangent and a secant intersect on a  at the pt. of tangency, then the measure of the  formed is half the measure of its intercepted arc. Multiply both sides by 2. Subtract 68 from both sides.

  20. 10.4 Other Angles Relationships in Circles Step 2 Find U V Example 5 Continued Thm. 11-5-3 Substitute the given values. Multiply both sides by 2. Add 66 to both sides.

  21. 10.4 Other Angles Relationships in Circles Find mLP Step 1 Find Step 2 Find Check It Out! Example 5

  22. 10.4 Other Angles Relationships in Circles Lesson Quiz: Part I Find each measure. 1. mFGJ 2. mHJK 41.5° 65°

  23. 10.4 Other Angles Relationships in Circles Lesson Quiz: Part II 3. An observer watches people riding a Ferris wheel that has 12 equally spaced cars. Find x. 30°

  24. 10.4 Other Angles Relationships in Circles Lesson Quiz: Part III 4. Find mCE. 12°

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