Question

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

Answer 1

Let's start by labeling each vertex A through F

Answer 2

how many edges attach to vertex A?

Answer 3

5?

Answer 4

yes

Answer 5

how about vertex B?

Answer 6

6

Answer 7

good, and vertex C?

Answer 8

6

Answer 9

correct, now vertex D

Answer 10

6

Answer 11

also correct, how about E?

Answer 12

6 again

Answer 13

and finally, vertex F

Answer 14

9

Answer 15

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

Answer 16

So wouldn't the sum be 38?

Answer 17

the sum is 38, yes

Answer 18

how many edges do you count?

Answer 19

19?

Answer 20

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