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10-6 Secants, Tangents, and Angle Measures

10-6 Secants, Tangents, and Angle Measures. You found measures of segments formed by tangents to a circle. . Find measures of angles formed by lines intersecting on or inside a circle. Find measures of angles formed by lines intersecting outside the circle. One line, One circle, Same plane….

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10-6 Secants, Tangents, and Angle Measures

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  1. 10-6 Secants, Tangents, and Angle Measures You found measures of segments formed by tangents to a circle. • Find measures of angles formed by lines intersecting on or inside a circle. • Find measures of angles formed by lines intersecting outside the circle.

  2. One line, One circle, Same plane…. The line intersects the circle in two points. It is a secant line.

  3. p. 741

  4. Use Intersecting Chords or Secants A. Find x. Theorem 10.12 Substitution Simplify. Answer:x = 82

  5. Use Intersecting Chords or Secants B. Find x. Step 1Find mVZW. Theorem 10.12 Substitution Simplify. Step 2Find mWZX. mWZX= 180 – mVZWDefinition of supplementary angles x = 180 – 79Substitution x = 101 Simplify. Answer:x = 101

  6. C. Find x. Theorem 10.12 Substitution Multiply each side by 2. Subtract 25 from each side. Answer:x = 95

  7. A. Find x. A. 92 B. 95 C. 98 D. 104

  8. C. Find x. A. 96 B. 99 C. 101 D. 104

  9. p. 742

  10. A. Find mQPS. Theorem 10.13 Substitute and simplify. Answer:mQPS= 125

  11. B. Answer: Use Intersecting Secants and Tangents Theorem 10.13 Substitution Multiply each side by 2.

  12. A. Find mFGI. A. 98 B. 108 C. 112.5 D. 118.5

  13. B. A. 99 B. 148.5 C. 162 D. 198

  14. p. 743

  15. A. Use Tangents and Secants that Intersect Outside a Circle Theorem 10.14 Substitution Multiply each side by 2. Subtract 141 from each side. Multiply each side by –1.

  16. B. Use Tangents and Secants that Intersect Outside a Circle Theorem 10.14 Substitution Multiply each side by 2. Add 140 to each side.

  17. A. A. 23 B. 26 C. 29 D. 32

  18. B. A. 194 B. 202 C. 210 D. 230

  19. p. 745

  20. 10-6 Assignment Page 746, 9-23 odd

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