Section 5-7
Diagonals and Angles of Polygons
Essential Questions


✤   How are polygons classified according to their sides?

✤   How do you find the sum of the angle me...
Vocabulary
1. Polygon:


2. Side:

3. Vertex:

4. Convex:

5. Concave:

6. Regular Polygon:


7. Diagonal:
Vocabulary
1. Polygon: A closed figure made by joining three or more segments at
     their endpoints

2. Side:

3. Vertex:...
Vocabulary
1. Polygon: A closed figure made by joining three or more segments at
     their endpoints

2. Side: One of the ...
Vocabulary
1. Polygon: A closed figure made by joining three or more segments at
     their endpoints

2. Side: One of the ...
Vocabulary
1. Polygon: A closed figure made by joining three or more segments at
     their endpoints

2. Side: One of the ...
Vocabulary
1. Polygon: A closed figure made by joining three or more segments at
     their endpoints

2. Side: One of the ...
Vocabulary
1. Polygon: A closed figure made by joining three or more segments at
     their endpoints

2. Side: One of the ...
Vocabulary
1. Polygon: A closed figure made by joining three or more segments at
     their endpoints

2. Side: One of the ...
Polygons and Their Sides

  5 sides:    6 sides:     7 sides:




  8 sides:    9 sides:     10 sides:
Polygons and Their Sides

  5 sides:    6 sides:     7 sides:
  Pentagon




  8 sides:    9 sides:     10 sides:
Polygons and Their Sides

  5 sides:    6 sides:     7 sides:
  Pentagon




  8 sides:    9 sides:     10 sides:
Polygons and Their Sides

  5 sides:     6 sides:    7 sides:
  Pentagon    Hexagon




  8 sides:     9 sides:    10 side...
Polygons and Their Sides

  5 sides:     6 sides:    7 sides:
  Pentagon    Hexagon




  8 sides:     9 sides:    10 side...
Polygons and Their Sides

  5 sides:     6 sides:     7 sides:
  Pentagon    Hexagon      Heptagon




  8 sides:     9 si...
Polygons and Their Sides

  5 sides:     6 sides:     7 sides:
  Pentagon    Hexagon      Heptagon




  8 sides:     9 si...
Polygons and Their Sides

  5 sides:     6 sides:     7 sides:
  Pentagon    Hexagon      Heptagon




  8 sides:     9 si...
Polygons and Their Sides

  5 sides:     6 sides:     7 sides:
  Pentagon    Hexagon      Heptagon




  8 sides:     9 si...
Polygons and Their Sides

  5 sides:     6 sides:     7 sides:
  Pentagon    Hexagon      Heptagon




  8 sides:     9 si...
Polygons and Their Sides

  5 sides:     6 sides:     7 sides:
  Pentagon    Hexagon      Heptagon




  8 sides:     9 si...
Polygons and Their Sides

  5 sides:     6 sides:     7 sides:
  Pentagon    Hexagon      Heptagon




  8 sides:     9 si...
Polygons and Their Sides

  5 sides:     6 sides:     7 sides:
  Pentagon    Hexagon      Heptagon




  8 sides:     9 si...
Polygons and Their Sides

  5 sides:               6 sides:    7 sides:
  Pentagon              Hexagon     Heptagon




 ...
Polygons and Their Sides

  5 sides:                  6 sides:                  7 sides:
  Pentagon                 Hexago...
Example 1
 Name each polygon by its number of sides and label as concave or
                            convex.
Example 1
 Name each polygon by its number of sides and label as concave or
                            convex.

         ...
Example 1
 Name each polygon by its number of sides and label as concave or
                            convex.

         ...
Example 1
 Name each polygon by its number of sides and label as concave or
                            convex.

         ...
Example 1
 Name each polygon by its number of sides and label as concave or
                            convex.

         ...
Example 1
 Name each polygon by its number of sides and label as concave or
                            convex.

         ...
Example 1
 Name each polygon by its number of sides and label as concave or
                            convex.

         ...
Example 1
 Name each polygon by its number of sides and label as concave or
                            convex.

         ...
Example 1
 Name each polygon by its number of sides and label as concave or
                            convex.

         ...
# of sides:       # of sides:

# of triangles:   # of triangles:

 Degrees:          Degrees:




  # of sides:       # of...
# of sides: 3     # of sides:

# of triangles:   # of triangles:

 Degrees:          Degrees:




  # of sides:       # of...
# of sides: 3       # of sides:

# of triangles: 1   # of triangles:

 Degrees:            Degrees:




  # of sides:     ...
# of sides: 3       # of sides:

# of triangles: 1   # of triangles:

 Degrees: 180°       Degrees:




  # of sides:     ...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles:

 Degrees: 180°       Degrees:




  # of sides:   ...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles:

 Degrees: 180°       Degrees:




  # of sides:   ...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees:




  # of sides: ...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




  # of si...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




  # of si...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




  # of si...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




  # of si...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




 # of sid...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




 # of sid...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




 # of sid...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




 # of sid...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




 # of sid...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




 # of sid...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




 # of sid...
# of sides: 3       # of sides: 4

# of triangles: 1   # of triangles: 2

 Degrees: 180°       Degrees: 360°




 # of sid...
Angle Sum of a Polygon:




Angle Measure of a Regular Polygon:
Angle Sum of a Polygon: The sum of the interior angles of a polygon
   with n sides is given by the formula




Angle Meas...
Angle Sum of a Polygon: The sum of the interior angles of a polygon
   with n sides is given by the formula




Angle Meas...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
Example 3
    Find the measure of each angle of a regular 14-gon.
Example 3
    Find the measure of each angle of a regular 14-gon.


         (n − 2)180°
      S=
              n
Example 3
    Find the measure of each angle of a regular 14-gon.


         (n − 2)180°
      S=
              n
        ...
Example 3
    Find the measure of each angle of a regular 14-gon.


         (n − 2)180°
      S=
              n
        ...
Example 3
    Find the measure of each angle of a regular 14-gon.


         (n − 2)180°
      S=
              n
        ...
Example 3
    Find the measure of each angle of a regular 14-gon.


         (n − 2)180°
      S=
              n
        ...
Homework
Homework



                           p. 224 #1-33 odd




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Integrated Math 2 Section 5-7

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  • Integrated Math 2 Section 5-7

    1. 1. Section 5-7 Diagonals and Angles of Polygons
    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, nature
    3. 3. Vocabulary 1. Polygon: 2. Side: 3. Vertex: 4. Convex: 5. Concave: 6. Regular Polygon: 7. Diagonal:
    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:
    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:
    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:
    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:
    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:
    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:
    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 side
    11. 11. Polygons and Their Sides 5 sides: 6 sides: 7 sides: 8 sides: 9 sides: 10 sides:
    12. 12. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon 8 sides: 9 sides: 10 sides:
    13. 13. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon 8 sides: 9 sides: 10 sides:
    14. 14. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon 8 sides: 9 sides: 10 sides:
    15. 15. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon 8 sides: 9 sides: 10 sides:
    16. 16. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides:
    17. 17. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides:
    18. 18. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon
    19. 19. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon
    20. 20. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon
    21. 21. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon
    22. 22. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon Decagon
    23. 23. Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon Decagon
    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:
    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 sides
    26. 26. Example 1 Name each polygon by its number of sides and label as concave or convex.
    27. 27. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave
    28. 28. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Pentagon
    29. 29. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon
    30. 30. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon
    31. 31. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex
    32. 32. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex Quadrilateral
    33. 33. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex Concave Quadrilateral
    34. 34. Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex Concave Quadrilateral Nonagon
    35. 35. # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:
    36. 36. # of sides: 3 # of sides: # of triangles: # of triangles: Degrees: Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:
    37. 37. # of sides: 3 # of sides: # of triangles: 1 # of triangles: Degrees: Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:
    38. 38. # of sides: 3 # of sides: # of triangles: 1 # of triangles: Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:
    39. 39. # of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:
    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:
    41. 41. # 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:
    42. 42. # 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:
    43. 43. # 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:
    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:
    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:
    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: 3 # of triangles: Degrees: Degrees:
    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: 540° Degrees:
    48. 48. # 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:
    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:
    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:
    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:
    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: 4 Degrees: 540° Degrees:
    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: 720°
    54. 54. Angle Sum of a Polygon: Angle Measure of a Regular Polygon:
    55. 55. 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:
    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: The measure of each interior angle of a regular polygon with n sides is given by the formula (n − 2)180° S= n
    57. 57. 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.
    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. A F B E C D
    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 10x F B 10x E C D
    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 3x + 8 E C 3x + 8 D
    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 7x - 22 3x + 8 E C 3x + 8 D
    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 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 D
    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 S = (n − 2)180° F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 D
    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 S = (6 − 2)180° 7x - 22 3x + 8 E C 3x + 8 D
    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° S = (4)180° 7x - 22 3x + 8 E C 3x + 8 D
    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 S = 720° E C 3x + 8 D
    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 The sum of all of the angles is 720° D
    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 F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 D
    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 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 D
    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° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 D
    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 41x − 18 = 720° 7x - 22 3x + 8 E C 3x + 8 D
    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° +18 +18 7x - 22 3x + 8 E C 3x + 8 D
    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 41x = 738 7x - 22 3x + 8 E C 3x + 8 D
    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 41 41 7x - 22 3x + 8 E C 3x + 8 D
    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 x = 18 3x + 8 D
    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 x = 18 F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 D
    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 10(18) = 7x - 22 3x + 8 E C 3x + 8 D
    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) = 180° 7x - 22 3x + 8 E C 3x + 8 D
    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° = m∠A = m∠B 7x - 22 3x + 8 E C 3x + 8 D
    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 3(18) + 8 = 7x - 22 3x + 8 E C 3x + 8 D
    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 = 62° 7x - 22 3x + 8 E C 3x + 8 D
    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° = m∠C = m∠D 7x - 22 3x + 8 E C 3x + 8 D
    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 7(18) - 22 = 7x - 22 3x + 8 E C 3x + 8 D
    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 = 104° 7x - 22 3x + 8 E C 3x + 8 D
    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° = m∠E 7x - 22 3x + 8 E C 3x + 8 D
    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 8(18) - 12 = 3x + 8 D
    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 = 132° 3x + 8 D
    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° = m∠F 3x + 8 D
    89. 89. Example 3 Find the measure of each angle of a regular 14-gon.
    90. 90. Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n
    91. 91. Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n (14 − 2)180° S= 14
    92. 92. 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
    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= 14 2160° S= 14
    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 S = 154 2 7 ° (12)180° S= 14 2160° S= 14
    95. 95. Homework
    96. 96. Homework p. 224 #1-33 odd “Liberty without learning is always in peril; learning without liberty is always in vain.” - John F. Kennedy

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