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Bellwork

Clickers. Bellwork. One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle Solve for x 2x 2 -13x-7=0. Bellwork Solution.

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Bellwork

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  1. Clickers Bellwork • One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle • Solve for x • 2x2-13x-7=0

  2. Bellwork Solution • One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle • Solve for x • 2x2-13x-7=0

  3. Section 10.5 Apply Other Angles Relationships in Circles

  4. The Concept • For the bulk of this chapter we’ve been dealing with the arc of circles • Today we’re going to finish out our discussion of arcs and angles

  5. Theorem Theorem 10.11 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc C This makes sense if we think about this in terms of an inscribed angle with only one leg D A B

  6. On your own • What is the measure of arc ADC A D 82o C B

  7. On your own • What is the measure of arc ABC A D 82o C B

  8. On your own • What is the measure of angle ACB, if arc CD measures 160o D A 35o C B

  9. Theorems Theorem 10.12 If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle A C x B D

  10. Example Find the measure of angle AEC 110o A C E B 96o D

  11. On your own • What is the measure of angle ABC D 225o A B E 255o C

  12. On your own • What is the measure of angle ABD D 148o B A E 30o C

  13. On your own • What is the measure of arc AC D A 121o 142o B E C

  14. Theorems Theorem 10.13 Angles Outside the Circle Theorem If a tangent and a secant, two tangents or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs C A B D

  15. Theorems Find the measure of angle ADB A C D 250o 110o B

  16. On your own B • What is the measure of angle ABD D A 30o E 86o C

  17. On your own • What is the measure of angle ADB A 195o 65o D B

  18. On your own • What is the measure of arc BD A 164o D 32o B

  19. On your own • What is the measure of arc AB A 120o D 22o B

  20. On your own • What is the measure of angle of E, if arc ABC is 200o A D B C E

  21. On your own A • What is the measure of angle of F? 110o B 80o D C F

  22. On your own A 110o • What is the measure of angle of F? 105o B D 35o C F

  23. Homework • 10.5 • 1-20, 22-25

  24. Most Important Points • Angle-Chord Relationships that intercept inside a circle • Angle relationship that intersects outside the circle

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