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11-5

11-5. Angle Relationships in Circles. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Geometry. Holt Geometry. 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°.

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11-5

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  1. 11-5 Angle Relationships in Circles Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

  2. 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. Objectives Find the measures of angles formed by lines that intersect circles. Use angle measures to solve problems.

  4. Example 1A: Using Tangent-Secant and Tangent-Chord Angles Find each measure. mEFH = 65°

  5. Example 1B: Using Tangent-Secant and Tangent-Chord Angles Find each measure.

  6. Check It Out! Example 1a Find each measure. mSTU = 83

  7. Check It Out! Example 1b Find each measure.

  8. Example 2: Finding Angle Measures Inside a Circle Find each measure. mAEB = 126

  9. Check It Out! Example 2a Find each angle measure. mABD

  10. Check It Out! Example 2b Find each angle measure. mRNM mRNM = 180° – MNQ mRNM = 180° – 158° = 22°

  11. Example 3: Finding Measures Using Tangents and Secants Find the value of x. = 40 = 63

  12. Check It Out! Example 3 Find the value of x. 50° = 83° – x x= 33°

  13. In the company logo shown, = 108°, and = 12°. What is mFKH? Example 4: Design Application

  14. 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

  15. 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.

  16. 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.

  17. Find mLP Step 1 Find Step 2 Find Check It Out! Example 5

  18. Lesson Quiz: Part I Find each measure. 1. mFGJ 2. mHJK 41.5° 65°

  19. Lesson Quiz: Part II 3. An observer watches people riding a Ferris wheel that has 12 equally spaced cars. Find x. 30°

  20. Lesson Quiz: Part III 4. Find mCE. 12°

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