Upcoming SlideShare
×

# Int Math 2 Section 5-7 1011

821 views

Published on

Diagonals and Angles of Polygons

Published in: Education
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
821
On SlideShare
0
From Embeds
0
Number of Embeds
331
Actions
Shares
0
3
0
Likes
0
Embeds 0
No embeds

No notes for slide

### 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