Diagonals and Angles of Polygons

1. Section 5-7
Diagonals and Angles of Polygons
Wed, Feb 02

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
Wed, Feb 02

3. Vocabulary
1. Polygon:
2. Side:
3. Vertex:
4. Convex:
5. Concave:
6. Regular Polygon:
7. Diagonal:
Wed, Feb 02

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. 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. 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. 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. 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. 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. 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
Wed, Feb 02

11. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
8 sides: 9 sides: 10 sides:
Wed, Feb 02

12. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon
8 sides: 9 sides: 10 sides:
Wed, Feb 02

13. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon
8 sides: 9 sides: 10 sides:
Wed, Feb 02

14. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon
8 sides: 9 sides: 10 sides:
Wed, Feb 02

15. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon
8 sides: 9 sides: 10 sides:
Wed, Feb 02

16. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon Heptagon
8 sides: 9 sides: 10 sides:
Wed, Feb 02

17. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon Heptagon
8 sides: 9 sides: 10 sides:
Wed, Feb 02

18. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon Heptagon
8 sides: 9 sides: 10 sides:
Octagon
Wed, Feb 02

19. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon Heptagon
8 sides: 9 sides: 10 sides:
Octagon
Wed, Feb 02

20. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon Heptagon
8 sides: 9 sides: 10 sides:
Octagon Nonagon
Wed, Feb 02

21. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon Heptagon
8 sides: 9 sides: 10 sides:
Octagon Nonagon
Wed, Feb 02

22. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon Heptagon
8 sides: 9 sides: 10 sides:
Octagon Nonagon Decagon
Wed, Feb 02

23. Polygons and Their Sides
5 sides: 6 sides: 7 sides:
Pentagon Hexagon Heptagon
8 sides: 9 sides: 10 sides:
Octagon Nonagon Decagon
Wed, Feb 02

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. 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
Wed, Feb 02

26. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Wed, Feb 02

27. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Wed, Feb 02

28. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Concave
Wed, Feb 02

29. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Concave
Pentagon
Wed, Feb 02

30. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Concave Convex
Pentagon
Wed, Feb 02

31. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Concave Convex
Pentagon Octagon
Wed, Feb 02

32. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Concave Convex
Pentagon Octagon
Convex
Wed, Feb 02

33. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Concave Convex
Pentagon Octagon
Convex
Quadrilateral
Wed, Feb 02

34. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Concave Convex
Pentagon Octagon
Convex Concave
Quadrilateral
Wed, Feb 02

35. Example 1
Name each polygon by its number of sides and label as concave or
convex.
Concave Convex
Pentagon Octagon
Convex Concave
Quadrilateral Nonagon
Wed, Feb 02

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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. # 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. Angle Sum of a Polygon:
Angle Measure of a Regular Polygon:
Wed, Feb 02

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. 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
Wed, Feb 02

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. 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
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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°
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

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
D
Wed, Feb 02

90. Example 3
Find the measure of each angle of a regular 14-gon.
Wed, Feb 02

91. Example 3
Find the measure of each angle of a regular 14-gon.
(n − 2)180°
S=
n
Wed, Feb 02

92. Example 3
Find the measure of each angle of a regular 14-gon.
(n − 2)180°
S=
n
(14 − 2)180°
S=
14
Wed, Feb 02

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
Wed, Feb 02

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=
14
Wed, Feb 02

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=
14
Wed, Feb 02

96. Problem Set
Wed, Feb 02

97. Problem Set
p. 224 #1-33 odd
“Liberty without learning is always in peril; learning without liberty is
always in vain.” - John F. Kennedy
Wed, Feb 02