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Section 5-7   Diagonals and Angles of PolygonsWed, Feb 02
Essential Questions   ✤    How are polygons classified according to their sides?   ✤    How do you find the sum of the angle...
Vocabulary    1. Polygon:    2. Side:    3. Vertex:    4. Convex:    5. Concave:    6. Regular Polygon:    7. Diagonal:Wed...
Vocabulary    1. Polygon: A closed figure made by joining three or more segments at         their endpoints    2. Side:    ...
Vocabulary    1. Polygon: A closed figure made by joining three or more segments at         their endpoints    2. Side: One...
Vocabulary    1. Polygon: A closed figure made by joining three or more segments at         their endpoints    2. Side: One...
Vocabulary    1. Polygon: A closed figure made by joining three or more segments at         their endpoints    2. Side: One...
Vocabulary    1. Polygon: A closed figure made by joining three or more segments at         their endpoints    2. Side: One...
Vocabulary    1. Polygon: A closed figure made by joining three or more segments at         their endpoints    2. Side: One...
Vocabulary    1. Polygon: A closed figure made by joining three or more segments at         their endpoints    2. Side: One...
Polygons and Their Sides              5 sides:   6 sides:   7 sides:              8 sides:   9 sides:   10 sides:Wed, Feb 02
Polygons and Their Sides              5 sides:   6 sides:   7 sides:              Pentagon              8 sides:   9 sides...
Polygons and Their Sides              5 sides:   6 sides:   7 sides:              Pentagon              8 sides:   9 sides...
Polygons and Their Sides              5 sides:    6 sides:   7 sides:              Pentagon   Hexagon              8 sides...
Polygons and Their Sides              5 sides:    6 sides:   7 sides:              Pentagon   Hexagon              8 sides...
Polygons and Their Sides              5 sides:    6 sides:    7 sides:              Pentagon   Hexagon     Heptagon       ...
Polygons and Their Sides              5 sides:    6 sides:    7 sides:              Pentagon   Hexagon     Heptagon       ...
Polygons and Their Sides              5 sides:    6 sides:    7 sides:              Pentagon   Hexagon     Heptagon       ...
Polygons and Their Sides              5 sides:    6 sides:    7 sides:              Pentagon   Hexagon     Heptagon       ...
Polygons and Their Sides              5 sides:    6 sides:    7 sides:              Pentagon   Hexagon     Heptagon       ...
Polygons and Their Sides              5 sides:    6 sides:    7 sides:              Pentagon   Hexagon     Heptagon       ...
Polygons and Their Sides              5 sides:    6 sides:    7 sides:              Pentagon   Hexagon     Heptagon       ...
Polygons and Their Sides              5 sides:    6 sides:    7 sides:              Pentagon   Hexagon     Heptagon       ...
Polygons and Their Sides              5 sides:               6 sides:    7 sides:              Pentagon              Hexag...
Polygons and Their Sides              5 sides:                  6 sides:                  7 sides:              Pentagon  ...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
Example 1          Name each polygon by its number of sides and label as concave or                                     co...
# of sides:       # of sides:              # of triangles:   # of triangles:               Degrees:          Degrees:     ...
# of sides: 3     # of sides:              # of triangles:   # of triangles:               Degrees:          Degrees:     ...
# of sides: 3       # of sides:              # of triangles: 1   # of triangles:               Degrees:            Degrees...
# of sides: 3       # of sides:              # of triangles: 1   # of triangles:               Degrees: 180°       Degrees...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles:               Degrees: 180°       Degre...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles:               Degrees: 180°       Degre...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
# of sides: 3       # of sides: 4              # of triangles: 1   # of triangles: 2               Degrees: 180°       Deg...
Angle Sum of a Polygon:       Angle Measure of a Regular Polygon:Wed, Feb 02
Angle Sum of a Polygon: The sum of the interior angles of a polygon        with n sides is given by the formula       Angl...
Angle Sum of a Polygon: The sum of the interior angles of a polygon        with n sides is given by the formula       Angl...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 2           In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8,          m∠E = 7x - 22, and m∠F = 8x - 12. Fin...
Example 3              Find the measure of each angle of a regular 14-gon.Wed, Feb 02
Example 3              Find the measure of each angle of a regular 14-gon.                   (n − 2)180°                S=...
Example 3              Find the measure of each angle of a regular 14-gon.                   (n − 2)180°                S=...
Example 3              Find the measure of each angle of a regular 14-gon.                   (n − 2)180°                S=...
Example 3              Find the measure of each angle of a regular 14-gon.                   (n − 2)180°                S=...
Example 3              Find the measure of each angle of a regular 14-gon.                   (n − 2)180°                S=...
Problem SetWed, Feb 02
Problem Set                                p. 224 #1-33 odd     “Liberty without learning is always in peril; learning wit...
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Int Math 2 Section 5-7 1011

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Diagonals and Angles of Polygons

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Transcript of "Int Math 2 Section 5-7 1011"

  1. 1. Section 5-7 Diagonals and Angles of PolygonsWed, Feb 02
  2. 2. Essential Questions ✤ How are polygons classified according to their sides? ✤ How do you find the sum of the angle measures of polygons? ✤ Where you’ll see this: ✤ Safety, hobbies, natureWed, Feb 02
  3. 3. Vocabulary 1. Polygon: 2. Side: 3. Vertex: 4. Convex: 5. Concave: 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
  4. 4. Vocabulary 1. Polygon: A closed figure made by joining three or more segments at their endpoints 2. Side: 3. Vertex: 4. Convex: 5. Concave: 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
  5. 5. Vocabulary 1. Polygon: A closed figure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: 4. Convex: 5. Concave: 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
  6. 6. Vocabulary 1. Polygon: A closed figure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: 5. Concave: 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
  7. 7. Vocabulary 1. Polygon: A closed figure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: When there are no indentations in a polygon 5. Concave: 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
  8. 8. Vocabulary 1. Polygon: A closed figure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: When there are no indentations in a polygon 5. Concave: When there is an indentation into a polygon 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
  9. 9. Vocabulary 1. Polygon: A closed figure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: When there are no indentations in a polygon 5. Concave: When there is an indentation into a polygon 6. Regular Polygon: A polygon where all the sides and angles are congruent 7. Diagonal:Wed, Feb 02
  10. 10. Vocabulary 1. Polygon: A closed figure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: When there are no indentations in a polygon 5. Concave: When there is an indentation into a polygon 6. Regular Polygon: A polygon where all the sides and angles are congruent 7. Diagonal: A segment that joins two vertices but is not a sideWed, Feb 02
  11. 11. Polygons and Their Sides 5 sides: 6 sides: 7 sides: 8 sides: 9 sides: 10 sides:Wed, Feb 02
  12. 12. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
  13. 13. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
  14. 14. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
  15. 15. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
  16. 16. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
  17. 17. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
  18. 18. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: OctagonWed, Feb 02
  19. 19. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: OctagonWed, Feb 02
  20. 20. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon NonagonWed, Feb 02
  21. 21. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon NonagonWed, Feb 02
  22. 22. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon DecagonWed, Feb 02
  23. 23. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon DecagonWed, Feb 02
  24. 24. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon Decagon Anything larger:Wed, Feb 02
  25. 25. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon Decagon Anything larger: n-gon, where n is the number of sidesWed, Feb 02
  26. 26. Example 1 Name each polygon by its number of sides and label as concave or convex.Wed, Feb 02
  27. 27. Example 1 Name each polygon by its number of sides and label as concave or convex.Wed, Feb 02
  28. 28. Example 1 Name each polygon by its number of sides and label as concave or convex. ConcaveWed, Feb 02
  29. 29. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave PentagonWed, Feb 02
  30. 30. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex PentagonWed, Feb 02
  31. 31. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon OctagonWed, Feb 02
  32. 32. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon ConvexWed, Feb 02
  33. 33. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex QuadrilateralWed, Feb 02
  34. 34. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex Concave QuadrilateralWed, Feb 02
  35. 35. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex Concave Quadrilateral NonagonWed, Feb 02
  36. 36. # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  37. 37. # of sides: 3 # of sides: # of triangles: # of triangles: Degrees: Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  38. 38. # of sides: 3 # of sides: # of triangles: 1 # of triangles: Degrees: Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  39. 39. # of sides: 3 # of sides: # of triangles: 1 # of triangles: Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  40. 40. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  41. 41. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  42. 42. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  43. 43. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  44. 44. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  45. 45. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  46. 46. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
  47. 47. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: 3 # of triangles: Degrees: Degrees:Wed, Feb 02
  48. 48. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
  49. 49. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
  50. 50. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
  51. 51. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
  52. 52. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
  53. 53. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: 4 Degrees: 540° Degrees:Wed, Feb 02
  54. 54. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: 4 Degrees: 540° Degrees: 720°Wed, Feb 02
  55. 55. Angle Sum of a Polygon: Angle Measure of a Regular Polygon:Wed, Feb 02
  56. 56. Angle Sum of a Polygon: The sum of the interior angles of a polygon with n sides is given by the formula Angle Measure of a Regular Polygon:Wed, Feb 02
  57. 57. Angle Sum of a Polygon: The sum of the interior angles of a polygon with n sides is given by the formula Angle Measure of a Regular Polygon: The measure of each interior angle of a regular polygon with n sides is given by the formula (n − 2)180° S= nWed, Feb 02
  58. 58. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle.Wed, Feb 02
  59. 59. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A F B E C DWed, Feb 02
  60. 60. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x F B 10x E C DWed, Feb 02
  61. 61. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x F B 10x 3x + 8 E C 3x + 8 DWed, Feb 02
  62. 62. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x F B 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  63. 63. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  64. 64. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  65. 65. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x S = (6 − 2)180° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  66. 66. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x S = (6 − 2)180° S = (4)180° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  67. 67. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x S = (6 − 2)180° S = (4)180° 7x - 22 3x + 8 S = 720° E C 3x + 8 DWed, Feb 02
  68. 68. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x S = (6 − 2)180° S = (4)180° 7x - 22 3x + 8 S = 720° E C 3x + 8 The sum of all of the angles is 720° DWed, Feb 02
  69. 69. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  70. 70. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  71. 71. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  72. 72. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  73. 73. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° +18 +18 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  74. 74. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° +18 +18 41x = 738 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  75. 75. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° +18 +18 41x = 738 41 41 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  76. 76. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° +18 +18 41x = 738 41 41 7x - 22 3x + 8 E C x = 18 3x + 8 DWed, Feb 02
  77. 77. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  78. 78. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  79. 79. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  80. 80. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  81. 81. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  82. 82. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  83. 83. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  84. 84. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  85. 85. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  86. 86. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° = m∠E 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
  87. 87. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° = m∠E 7x - 22 3x + 8 E C 8(18) - 12 = 3x + 8 DWed, Feb 02
  88. 88. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° = m∠E 7x - 22 3x + 8 E C 8(18) - 12 = 132° 3x + 8 DWed, Feb 02
  89. 89. Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then find the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° = m∠E 7x - 22 3x + 8 E C 8(18) - 12 = 132° = m∠F 3x + 8 DWed, Feb 02
  90. 90. Example 3 Find the measure of each angle of a regular 14-gon.Wed, Feb 02
  91. 91. Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= nWed, Feb 02
  92. 92. Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n (14 − 2)180° S= 14Wed, Feb 02
  93. 93. Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n (14 − 2)180° S= 14 (12)180° S= 14Wed, Feb 02
  94. 94. Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n (14 − 2)180° S= 14 (12)180° S= 14 2160° S= 14Wed, Feb 02
  95. 95. Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n (14 − 2)180° S= 14 S = 154 2 7 ° (12)180° S= 14 2160° S= 14Wed, Feb 02
  96. 96. Problem SetWed, Feb 02
  97. 97. Problem Set p. 224 #1-33 odd “Liberty without learning is always in peril; learning without liberty is always in vain.” - John F. KennedyWed, Feb 02
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