MathPlotAI Logo MathPlotAI

Exterior Angles in Convex Polygons

Exterior Angles in Convex Polygons
Loading the math board and drawing, please wait…
2019-04-25 01:11
PolygonAngleGeometric Construction
This example demonstrates the properties and calculation of exterior angles in convex polygons. Key math concepts include the exterior angle sum theorem and the relationship between interior and exterior angles. It is constructed using commands like Segment, Polygon, DynamicCoordinates, Sequence, Angle, Sum, and TableText to draw polygons and calculate exterior angle sums. Suitable for high school mathematics education to understand polygonal geometric properties and function applications.

GeoGebra Commands & Parameters

  1. Segment(C39, E39) → F39
  2. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  3. DynamicCoordinates(A5, If[D5, x(A5), x(C5)], If[D5, y(A5), y(C5)]) → B5
  4. DynamicCoordinates(A6, If[D6, x(A6), x(C6)], If[D6, y(A6), y(C6)]) → B6
  5. DynamicCoordinates(A7, If[D7, x(A7), x(C7)], If[D7, y(A7), y(C7)]) → B7
  6. DynamicCoordinates(A8, If[D8, x(A8), x(C8)], If[D8, y(A8), y(C8)]) → B8
  7. DynamicCoordinates(A9, If[D9, x(A9), x(C9)], If[D9, y(A9), y(C9)]) → B9
  8. DynamicCoordinates(A10, If[D10, x(A10), x(C10)], If[D10, y(A10), y(C10)]) → B10
  9. DynamicCoordinates(A11, If[D11, x(A11), x(C11)], If[D11, y(A11), y(C11)]) → B11
  10. DynamicCoordinates(A12, If[D12, x(A12), x(C12)], If[D12, y(A12), y(C12)]) → B12
  11. DynamicCoordinates(A13, If[D13, x(A13), x(C13)], If[D13, y(A13), y(C13)]) → B13
  12. DynamicCoordinates(A4, If[D4, x(A4), x(C4)], If[D4, y(A4), y(C4)]) → B4
  13. DynamicCoordinates(A18, If[D18, x(A18), x(C18)], If[D18, y(A18), y(C18)]) → B18
  14. DynamicCoordinates(A19, If[D19, x(A19), x(C19)], If[D19, y(A19), y(C19)]) → B19
  15. DynamicCoordinates(A20, If[D20, x(A20), x(C20)], If[D20, y(A20), y(C20)]) → B20
  16. DynamicCoordinates(A21, If[D21, x(A21), x(C21)], If[D21, y(A21), y(C21)]) → B21
  17. DynamicCoordinates(A22, If[D22, x(A22), x(C22)], If[D22, y(A22), y(C22)]) → B22
  18. DynamicCoordinates(A23, If[D23, x(A23), x(C23)], If[D23, y(A23), y(C23)]) → B23
  19. DynamicCoordinates(A24, If[D24, x(A24), x(C24)], If[D24, y(A24), y(C24)]) → B24
  20. DynamicCoordinates(A25, If[D25, x(A25), x(C25)], If[D25, y(A25), y(C25)]) → B25
  21. DynamicCoordinates(A26, If[D26, x(A26), x(C26)], If[D26, y(A26), y(C26)]) → B26
  22. DynamicCoordinates(A31, If[D31, x(A31), x(C31)], If[D31, y(A31), y(C31)]) → B31
  23. DynamicCoordinates(A32, If[D32, x(A32), x(C32)], If[D32, y(A32), y(C32)]) → B32
  24. DynamicCoordinates(A33, If[D33, x(A33), x(C33)], If[D33, y(A33), y(C33)]) → B33
  25. DynamicCoordinates(A29, If[D29, x(A29), x(C29)], If[D29, y(A29), y(C29)]) → B29
  26. DynamicCoordinates(A30, If[D30, x(A30), x(C30)], If[D30, y(A30), y(C30)]) → B30
  27. DynamicCoordinates(A34, If[D34, x(A34), x(C34)], If[D34, y(A34), y(C34)]) → B34
  28. DynamicCoordinates(A35, If[D35, x(A35), x(C35)], If[D35, y(A35), y(C35)]) → B35
  29. DynamicCoordinates(A36, If[D36, x(A36), x(C36)], If[D36, y(A36), y(C36)]) → B36
  30. DynamicCoordinates(A39, If[D39, x(A39), x(C39)], If[D39, y(A39), y(C39)]) → B39
  31. DynamicCoordinates(A40, If[D40, x(A40), x(C40)], If[D40, y(A40), y(C40)]) → B40
  32. DynamicCoordinates(A41, If[D41, x(A41), x(C41)], If[D41, y(A41), y(C41)]) → B41
  33. DynamicCoordinates(A42, If[D42, x(A42), x(C42)], If[D42, y(A42), y(C42)]) → B42
  34. DynamicCoordinates(A43, If[D43, x(A43), x(C43)], If[D43, y(A43), y(C43)]) → B43
  35. DynamicCoordinates(A44, If[D44, x(A44), x(C44)], If[D44, y(A44), y(C44)]) → B44
  36. DynamicCoordinates(A45, If[D45, x(A45), x(C45)], If[D45, y(A45), y(C45)]) → B45
  37. DynamicCoordinates(A49, If[D49, x(A49), x(C49)], If[D49, y(A49), y(C49)]) → B49
  38. DynamicCoordinates(A50, If[D50, x(A50), x(C50)], If[D50, y(A50), y(C50)]) → B50
  39. DynamicCoordinates(A51, If[D51, x(A51), x(C51)], If[D51, y(A51), y(C51)]) → B51
  40. DynamicCoordinates(A52, If[D52, x(A52), x(C52)], If[D52, y(A52), y(C52)]) → B52
  41. DynamicCoordinates(A53, If[D53, x(A53), x(C53)], If[D53, y(A53), y(C53)]) → B53
  42. DynamicCoordinates(A57, If[D57, x(A57), x(C57)], If[D57, y(A57), y(C57)]) → B57
  43. DynamicCoordinates(A58, If[D58, x(A58), x(C58)], If[D58, y(A58), y(C58)]) → B58
  44. DynamicCoordinates(A59, If[D59, x(A59), x(C59)], If[D59, y(A59), y(C59)]) → B59
  45. DynamicCoordinates(A60, If[D60, x(A60), x(C60)], If[D60, y(A60), y(C60)]) → B60
  46. DynamicCoordinates(A61, If[D61, x(A61), x(C61)], If[D61, y(A61), y(C61)]) → B61
  47. DynamicCoordinates(A64, If[D64, x(A64), x(C64)], If[D64, y(A64), y(C64)]) → B64
  48. DynamicCoordinates(A65, If[D65, x(A65), x(C65)], If[D65, y(A65), y(C65)]) → B65
  49. DynamicCoordinates(A66, If[D66, x(A66), x(C66)], If[D66, y(A66), y(C66)]) → B66
  50. DynamicCoordinates(A67, If[D67, x(A67), x(C67)], If[D67, y(A67), y(C67)]) → B67
  51. DynamicCoordinates(A54, If[D54, x(A54), x(C54)], If[D54, y(A54), y(C54)]) → B54
  52. Sequence(If[i ≟ numSides - 1, (("\cellcolor{#fff59d}{" * Element[col1, i]) * "}"), ("" * Element[col1, i])], i, 1, maxSides - 1) → col1Display
  53. Sequence(If[i ≟ numSides - 1, (("\cellcolor{#fff59d}{" * Element[col2, i]) * "}"), Element[col2, i]], i, 1, maxSides - 1) → col2Display
  54. Segment(C4, E4) → F4
  55. Segment(C5, E5) → F5
  56. Segment(C6, E6) → F6
  57. Segment(C7, E7) → F7
  58. Segment(C8, E8) → F8
  59. Segment(C9, E9) → F9
  60. Segment(C10, E10) → F10
  61. Segment(C11, E11) → F11
  62. Segment(C12, E12) → F12
  63. Segment(C13, E13) → F13
  64. Polygon({C4, C5, C6, C7, C8, C9, C10, C11, C12, C13}) → B3
  65. Angle(E4, C4, C5) → G4
  66. Angle(E5, C5, C6) → G5
  67. Angle(E6, C6, C7) → G6
  68. Angle(E7, C7, C8) → G7
  69. Angle(E8, C8, C9) → G8
  70. Angle(E9, C9, C10) → G9
  71. Angle(E10, C10, C11) → G10
  72. Angle(E11, C11, C12) → G11
  73. Angle(E12, C12, C13) → G12
  74. Angle(E13, C13, C4) → G13
  75. Segment(C18, E18) → F18
  76. Segment(C19, E19) → F19
  77. Segment(C20, E20) → F20
  78. Segment(C21, E21) → F21
  79. Segment(C22, E22) → F22
  80. Segment(C23, E23) → F23
  81. Segment(C24, E24) → F24
  82. Segment(C25, E25) → F25
  83. Segment(C26, E26) → F26
  84. Polygon(C18:C26) → B17
  85. Angle(E18, C18, C19) → G18
  86. Angle(E19, C19, C20) → G19
  87. Angle(E20, C20, C21) → G20
  88. Angle(E21, C21, C22) → G21
  89. Angle(E22, C22, C23) → G22
  90. Angle(E23, C23, C24) → G23
  91. Angle(E24, C24, C25) → G24
  92. Angle(E25, C25, C26) → G25
  93. Angle(E26, C26, C18) → G26
  94. Polygon(C29:C36) → B28
  95. Segment(C29, E29) → F29
  96. Segment(C30, E30) → F30
  97. Segment(C31, E31) → F31
  98. Segment(C32, E32) → F32
  99. Segment(C33, E33) → F33
  100. Segment(C34, E34) → F34
  101. Segment(C35, E35) → F35
  102. Segment(C36, E36) → F36
  103. Angle(E30, C30, C31) → G30
  104. Angle(E31, C31, C32) → G31
  105. Angle(E32, C32, C33) → G32
  106. Angle(E33, C33, C34) → G33
  107. Angle(E34, C34, C35) → G34
  108. Angle(E35, C35, C36) → G35
  109. Angle(E36, C36, C29) → G36
  110. Angle(E29, C29, C30) → G29
  111. Polygon(C39:C45) → B38
  112. Segment(C40, E40) → F40
  113. Segment(C41, E41) → F41
  114. Segment(C42, E42) → F42
  115. Segment(C43, E43) → F43
  116. Segment(C44, E44) → F44
  117. Segment(C45, E45) → F45
  118. Angle(E39, C39, C40) → G39
  119. Angle(E40, C40, C41) → G40
  120. Angle(E41, C41, C42) → G41
  121. Angle(E42, C42, C43) → G42
  122. Angle(E43, C43, C44) → G43
  123. Angle(E44, C44, C45) → G44
  124. Angle(E45, C45, C39) → G45
  125. Sum(H29:H34) → test
  126. Polygon(C49:C54) → B48
  127. Segment(C49, E49) → F49
  128. Segment(C50, E50) → F50
  129. Segment(C51, E51) → F51
  130. Segment(C52, E52) → F52
  131. Segment(C53, E53) → F53
  132. Segment(C54, E54) → F54
  133. Angle(E49, C49, C50) → G49
  134. Angle(E50, C50, C51) → G50
  135. Angle(E51, C51, C52) → G51
  136. Angle(E52, C52, C53) → G52
  137. Angle(E53, C53, C54) → G53
  138. Angle(E54, C54, C49) → G54
  139. Polygon(C57:C61) → B56
  140. Segment(C57, E57) → F57
  141. Segment(C58, E58) → F58
  142. Segment(C59, E59) → F59
  143. Segment(C60, E60) → F60
  144. Segment(C61, E61) → F61
  145. Angle(E57, C57, C58) → G57
  146. Angle(E58, C58, C59) → G58
  147. Angle(E59, C59, C60) → G59
  148. Angle(E60, C60, C61) → G60
  149. Angle(E61, C61, C57) → G61
  150. Polygon(C64:C67) → B63
  151. Segment(C64, E64) → F64
  152. Segment(C65, E65) → F65
  153. Segment(C66, E66) → F66
  154. Segment(C67, E67) → F67
  155. Angle(E64, C64, C65) → G64
  156. Angle(E65, C65, C66) → G65
  157. Angle(E66, C66, C67) → G66
  158. Angle(E67, C67, C64) → G67
  159. TableText({col1Display, col2Display}, "vc|_") → dataTable

AI Drawing Prompt Reference

Draw a convex polygon and show its exterior angle sum. The figure should include the polygon itself, its vertices, the connecting edges, and the exterior angles at each vertex. The construction order is: first draw a reference line segment, then generate the polygon's vertices using dynamic coordinates, connect these vertices to form the polygon, and label the exterior angles. Ensure the figure is clear to help understand the relationship between interior and exterior angles and the application of the exterior angle sum theorem.
The prompt above was compiled from the original drawing commands and is for reference only.