Degrees 3

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Precalculus

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Degrees

Degrees 3

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Question 1 of 3

1. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Degree of Vertex $G$ $G$ $=$ $=$ (6)
  
  $(i i)$ $(ii)$ Degree of Vertex $C$ $C$ $=$ $=$ (3)
  
  $(i i i)$ $(iii)$ Degree of Vertex $F$ $F$ $=$ $=$ (2)
  
  $(i v)$ $(iv)$ Total number of Edges $=$ $=$ (11)
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A degree is the number of edges that connects to a vertex.

$(i)$ $(i)$    Degrees of Vertex $G$ $G$

Count the edges connecting to vertex $G$ $G$ .

There are $6$ $6$ edges connected to vertex $G$ $G$ . Therefore, the degree of vertex $G$ $G$ is $6$ $6$ .

$(i i)$ $(ii)$    Degrees of Vertex $C$ $C$

Count the edges connecting to vertex $C$ $C$ .

There are $3$ $3$ edges connected to vertex $C$ $C$ . Therefore, the degree of vertex $C$ $C$ is $3$ $3$ .

$(i i i)$ $(iii)$    Degrees of Vertex $F$ $F$

Count the edges connecting to vertex $F$ $F$ .

There are $2$ $2$ edges connected to vertex $F$ $F$ . Therefore, the degree of vertex $F$ $F$ is $2$ $2$ .

$(i v)$ $(iv)$    Total number of Edges

Get the number of edges, or the lines connecting the vertices.

There are $11$ $11$ lines connecting the vertices. Therefore, the total number of edges is $11$ $11$ .

$(i)$ $(i)$ Degree of $G = 6$ $G=6$

$(i i)$ $(ii)$ Degree of $C = 3$ $C=3$

$(i i i)$ $(iii)$ Degree of $F = 2$ $F=2$

$(i v)$ $(iv)$ Total number of Edges $= 11$ $=11$
Question 2 of 3

2. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Number of Vertices $=$ $=$ (9)
  
  $(i i)$ $(ii)$ Degree of Edges $=$ $=$ (13)
  
  $(i i i)$ $(iii)$ Number of Odd Vertices $=$ $=$ (6)
  
  $(i v)$ $(iv)$ Number of Even Vertices $=$ $=$ (3)
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A degree is the number of edges that connects to a vertex.

$(i)$ $(i)$    Number of Vertices

Count the vertices or points in the figure.

The figure has $9$ $9$ points in it. Therefore, the total number of vertices is $9$ $9$ .

$(i i)$ $(ii)$    Number of Edges

Get the number of edges, or the lines connecting the vertices.

There are $13$ $13$ lines connecting the vertices. Therefore, the total number of edges is $13$ $13$ .

$(i i i)$ $(iii)$    Number of Odd Vertices

Find the degree of all the vertices and count the vertices with an odd number of degrees.

Vertices $A$ $A$ , $B$ $B$ , $D$ $D$ , $F$ $F$ , $H$ $H$ , and $I$ $I$ all have odd number of degrees. Therefore, the number of odd vertices is $6$ $6$ .

$(i v)$ $(iv)$    Number of Even Degrees

Find the degree of all the vertices and count the vertices with an even number of degrees.

Vertices $C$ $C$ , $E$ $E$ , and $G$ $G$ all have even number of degrees. Therefore, the number of even vertices is $3$ $3$ .

$(i)$ $(i)$ Number of Vertices $= 9$ $=9$

$(i i)$ $(ii)$ Number of Edges $= 13$ $=13$

$(i i i)$ $(iii)$ Number of Odd Vertices $= 6$ $=6$

$(i v)$ $(iv)$ Number of Even Vertices $= 3$ $=3$
Question 3 of 3

3. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Degree of Vertex $A$ $A$ $=$ $=$ (5)
  
  $(i i)$ $(ii)$ Degree of Vertex $C$ $C$ $=$ $=$ (4)
  
  $(i i i)$ $(iii)$ Number of Odd Vertices $=$ $=$ (4)
  
  $(i v)$ $(iv)$ Total Number of Edges $=$ $=$ (10)
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A degree is the number of edges that connects to a vertex.

$(i)$ $(i)$    Degrees of Vertex $A$ $A$

Count the edges connecting to vertex $A$ $A$ .

Notice that there is a loop connected to vertex $A$ $A$ .

A loop consists of $2$ $2$ edges. Therefore, there are a total of $5$ $5$ edges connected to vertex $A$ $A$ . Therefore, the degree of vertex $A$ $A$ is $5$ $5$ .

$(i i)$ $(ii)$    Degrees of Vertex $C$ $C$

Count the edges connecting to vertex $C$ $C$ .

There are $4$ $4$ edges connected to vertex $C$ $C$ . Therefore, the degree of vertex $C$ $C$ is $4$ $4$ .

$(i i i)$ $(iii)$    Number of Odd Vertices

Find the degree of all the vertices and count the vertices with an odd number of degrees.

Vertices $A$ $A$ , $B$ $B$ , $D$ $D$ , and $E$ $E$ all have odd number of degrees. Therefore, the number of odd vertices is $4$ $4$ .

$(i v)$ $(iv)$    Total number of Edges

Get the number of edges, or the lines connecting the vertices.

There are $10$ $10$ lines connecting the vertices. Therefore, the total number of edges is $10$ $10$ .

$(i)$ $(i)$ Degree of $A = 5$ $A=5$

$(i i)$ $(ii)$ Degree of $A = 4$ $A=4$

$(i i i)$ $(iii)$ Number of Odd Vertices $= 4$ $=4$

$(i v)$ $(iv)$ Total number of Edges $= 10$ $=10$

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