Degrees 1

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Precalculus

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Degrees

Degrees 1

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Question 1 of 4

1. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Degree of Vertex $A$ $A$ $=$ $=$ (2)
  
  $(i i)$ $(ii)$ Degree of Vertex $D$ $D$ $=$ $=$ (3)
  
  $(i i i)$ $(iii)$ Number of Vertices with $Degree 4$ $\text(Degree) 4$ $=$ $=$ (3)
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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 $A$ $A$ .

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

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

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

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

$(i i i)$ $(iii)$    Vertices with $Degree 4$ $\text(Degree) 4$

Get the degrees of all the vertices and count how many vertices has $4$ $4$ edges connecting to them.

The vertices $B$ $B$ , $E$ $E$ , and $F$ $F$ all have $4$ $4$ edges connecting to them. Therefore, there are $3$ $3$ vertices that are $degree 4$ $\text(degree) 4$ .

$(i)$ $(i)$ Degree of $A = 2$ $A=2$

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

$(i i i)$ $(iii)$ Vertices with $Degree 4 = 3$ $\text(Degree 4)=3$
Question 2 of 4

2. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Degree of Vertex $A$ $A$ $=$ $=$ (3)
  
  $(i i)$ $(ii)$ Degree of Vertex $B$ $B$ $=$ $=$ (3)
  
  $(i i i)$ $(iii)$ Degree of Vertex $C$ $C$ $=$ $=$ (2)
  
  $(i v)$ $(iv)$ Degree of Vertex $D$ $D$ $=$ $=$ (4)
  
  $(v)$ $(v)$ Degree of Vertex $E$ $E$ $=$ $=$ (2)
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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 $A$ $A$ .

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

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

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

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

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

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

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

$(i v)$ $(iv)$    Degrees of Vertex $D$ $D$

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

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

$(v)$ $(v)$    Degrees of Vertex $E$ $E$

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

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

$(i)$ $(i)$ Degree of $A = 3$ $A=3$

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

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

$(i v)$ $(iv)$ Degree of $D = 4$ $D=4$

$(v)$ $(v)$ Degree of $E = 2$ $E=2$
Question 3 of 4

3. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Degree of Vertex $P$ $P$ $=$ $=$ (2)
  
  $(i i)$ $(ii)$ Degree of Vertex $Q$ $Q$ $=$ $=$ (4)
  
  $(i i i)$ $(iii)$ Degree of Vertex $R$ $R$ $=$ $=$ (2)
  
  $(i v)$ $(iv)$ Degree of Vertex $S$ $S$ $=$ $=$ (2)
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A degree is the number of edges that connects to a vertex.

$(i)$ $(i)$    Degrees of Vertex $P$ $P$

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

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

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

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

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

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

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

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

$(i v)$ $(iv)$    Degrees of Vertex $S$ $S$

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

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

$(i)$ $(i)$ Degree of $P = 2$ $P=2$

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

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

$(i v)$ $(iv)$ Degree of $S = 2$ $S=2$
Question 4 of 4

4. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Degree of Vertex $A$ $=$ (4)
  
  $(ii)$ Degree of Vertex $B$ $=$ (2)
  
  $(iii)$ Degree of Vertex $C$ $=$ (5)
  
  $(iv)$ Degree of Vertex $D$ $=$ (2)
  
  $(v)$ Degree of Vertex $E$ $=$ (1)
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A degree is the number of edges that connects to a vertex.

$(i)$    Degrees of Vertex $A$

Count the edges connecting to vertex $A$ .

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

$(ii)$    Degrees of Vertex $B$

Count the edges connecting to vertex $B$ .

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

$(iii)$    Degrees of Vertex $C$

Count the edges connecting to vertex $C$ .

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

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

$(iv)$    Degrees of Vertex $D$

Count the edges connecting to vertex $D$ .

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

$(v)$    Degrees of Vertex $E$

Count the edges connecting to vertex $E$ .

There is $1$ edge connected to vertex $E$ . Therefore, the degree of vertex $E$ is $1$ .

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

$(ii)$ Degree of $B=2$

$(iii)$ Degree of $C=5$

$(iv)$ Degree of $D=2$

$(v)$ Degree of $E=1$

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