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warpedkitten

  • one year ago

For the given figure, find the number of edges and the sum of the degrees of the vertices. a. number of edges: 18 sum of degrees of vertices: 38 b. number of edges: 19 sum of degrees of vertices: 38 c. number of edges: 6 sum of degrees of vertices: 40 d. number of edges: 18 sum of degrees of vertices: 6

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  1. warpedkitten
    • one year ago
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  2. jim_thompson5910
    • one year ago
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    Let's start by labeling each vertex A through F

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  3. jim_thompson5910
    • one year ago
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    how many edges attach to vertex A?

  4. warpedkitten
    • one year ago
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    5?

  5. jim_thompson5910
    • one year ago
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    yes

  6. jim_thompson5910
    • one year ago
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    how about vertex B?

  7. warpedkitten
    • one year ago
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    6

  8. jim_thompson5910
    • one year ago
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    good, and vertex C?

  9. warpedkitten
    • one year ago
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    6

  10. jim_thompson5910
    • one year ago
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    correct, now vertex D

  11. warpedkitten
    • one year ago
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    6

  12. jim_thompson5910
    • one year ago
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    also correct, how about E?

  13. warpedkitten
    • one year ago
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    6 again

  14. jim_thompson5910
    • one year ago
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    and finally, vertex F

  15. warpedkitten
    • one year ago
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    9

  16. jim_thompson5910
    • one year ago
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    so we have degree of A: 5 degree of B: 6 degree of C: 6 degree of D: 6 degree of E: 6 degree of F: 9

  17. warpedkitten
    • one year ago
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    So wouldn't the sum be 38?

  18. jim_thompson5910
    • one year ago
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    the sum is 38, yes

  19. jim_thompson5910
    • one year ago
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    how many edges do you count?

  20. warpedkitten
    • one year ago
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    19?

  21. jim_thompson5910
    • one year ago
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    I'm counting 19 as well 5 edges in the outer circle 5 edges in the pentagon 8 curved edges on the inside (2*4 = 8) leading to the center 1 straight edge on the very inside leading to the center 5+5+8+1 = 19

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