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The Great Angle Chase

The Great Angle Chase. There are many different pathways that lead to the same destination. Here is just one of them …. G. U. P. 35 . T. K. L. 25 . J. M. 100 . O. I. H. N. Q. S. R. Aim: To write in the size of every angle. G. U. P. 35 . T. K. L. 25 . J. M.

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The Great Angle Chase

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  1. The Great Angle Chase There are many different pathways that lead to the same destination. Here is just one of them …

  2. G U P 35 T K L 25 J M 100 O I H N Q S R Aim: To write in the size of every angle.

  3. G U P 35 T K L 25 J M 100 O I H N Q S R • Look for the angle between a tangent and a chord. • Locate the angles in the alternate segment. 25 25

  4. G U P 35 T K L 25 J M 100 O I H N Q S R 25 25

  5. G U P 35 T K L 25 J M 100 O I H N Q S R Look for angles in the same segment. 25 35 25

  6. G U P 35 T K L 25 J M 100 O I H N Q S R 25 35 25

  7. G U P 35 T K L 25 J M 100 O I H N Q S R Look for angles standing on equal chords. 25 25 25 35 25

  8. G U P 35 T K L 25 J M 100 O I H N Q S R 25 25 25 35 25

  9. G U P 35 T K L 25 J M 100 O I H N Q S R Look for right angles: • The angle between a tangent and a radius • The angle in a semicircle 25 65 25 65 40 25 35 25

  10. G U P 35 T K L 25 J M 100 O I H N Q S R 25 65 25 65 40 25 35 25

  11. G U P 35 T K L 25 J M 100 O I H N Q S R Look for triangles: 25 Angle sum 65 55 55 25 65 40 25 35 40 75 25

  12. G U P 35 T K L 25 J M 100 O I H N Q S R Look for triangles: Angle sum 25 65 55 55 25 65 40 25 75 120 35 40 75 25

  13. G U P 35 T K L 25 J M 100 O I H N Q S R Look for triangles: 25 65 • Angle sum • Exterior angle 55 55 125 25 65 40 25 75 120 35 40 75 25

  14. G U P 35 T K L 25 J M 100 O I H N Q S R Look for triangles: 25 65 • Angle sum • Exterior angle 55 60 55 125 25 65 40 25 75 120 35 40 75 25

  15. G U P 35 T K L 25 J M 100 O I H N Q S R Look for vertically opposite angles and angles at a point. 25 65 120 60 55 125 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 35 40 75 25

  16. G U P 35 T K L 25 J M 100 O I H N Q S R And there’s another triangle. 25 65 120 60 55 125 15 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 35 40 75 25

  17. G U P 35 T K L 25 J M 100 O I H N Q S R And then another pair of angles in the same segment. 25 65 120 60 55 125 15 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 35 40 75 25 15

  18. G U P 35 T K L 25 J M 100 O I H N Q S R Some more right angles. 25 65 40 120 60 55 125 15 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 35 40 75 25 75 15

  19. G U P 35 T K L 25 J M 100 O I H N Q S R Aha! A cyclic quadrilateral. 25 65 40 120 60 55 125 15 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 35 40 80 75 25 75 15

  20. G U P 35 T K L 25 J M 100 O I H N Q S R More angles at a point. 25 65 40 120 60 55 125 15 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 100 35 80 40 80 100 75 25 75 15

  21. G U P 35 T K L 25 J M 100 O I H N Q S R 25 65 40 120 60 55 125 15 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 100 35 80 40 80 100 75 25 75 15

  22. G U P 35 T K L 25 J M 100 O I H N Q S R Another angle between a tangent and a chord. 25 65 40 120 60 55 125 15 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 100 35 80 40 80 40 100 75 25 75 15

  23. G U P 35 T K L 25 J M 100 O I H N Q S R A cyclic quadrilateral. 25 65 40 120 60 55 125 15 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 100 35 80 40 80 40 100 75 65 25 75 15

  24. G U P 35 T K L 25 J M 100 O I H N Q S R And we’re done! 25 65 40 120 60 55 125 15 60 55 125 120 25 65 40 105 75 25 75 60 105 120 120 80 100 60 80 100 35 80 40 80 40 100 75 65 25 75 15

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