Degrees 2

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Precalculus

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Degrees

Degrees 2

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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 $B$ $B$ $=$ $=$ (4)
  
  $(i i)$ $(ii)$ Number of Vertices with $Degree 3$ $\text(Degree) 3$ $=$ $=$ (2)
  
  $(i i i)$ $(iii)$ Sum of the Degrees $=$ $=$ (18)
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A degree is the number of edges that connects to a vertex.

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

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

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

$(i i)$ $(ii)$    Vertices with $Degree 3$ $\text(Degree) 3$

Get the degrees of all the vertices and count how many vertices has $3$ $3$ edges connecting to them.

The vertices $C$ $C$ and $F$ $F$ both have $3$ $3$ edges connecting to them. Therefore, there are $2$ $2$ vertices that are $degree 3$ $\text(degree) 3$ .

$(i i i)$ $(iii)$    Sum of the degrees

Get the degrees of all the vertices and add them to get the sum of the degrees.

Sum of Degrees $=$ $=$ $4 + 3 + 2 + 4 + 3 + 2$ $4+3+2+4+3+2$

$=$ $=$ $18$ $18$

Therefore, the sum of the degrees is $18$ $18$ .

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

$(i i)$ $(ii)$ Vertices with $Degree 3 = 2$ $\text(Degree 3)=2$

$(i i i)$ $(iii)$ Sum of Degrees $= 18$ $=18$
Question 2 of 4

2. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Degree of Vertex $B$ $B$ $=$ $=$ (4)
  
  $(i i)$ $(ii)$ Number of Vertices with $Degree 3$ $\text(Degree) 3$ $=$ $=$ (4)
  
  $(i i i)$ $(iii)$ Sum of the Degrees $=$ $=$ (24)
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A degree is the number of edges that connects to a vertex.

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

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

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

$(i i)$ $(ii)$    Vertices with $Degree 3$ $\text(Degree) 3$

Get the degrees of all the vertices and count how many vertices has $3$ $3$ edges connecting to them.

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

$(i i i)$ $(iii)$    Sum of the degrees

Get the degrees of all the vertices and add them to get the sum of the degrees.

Sum of Degrees $=$ $=$ $2 + 4 + 3 + 2 + 3 + 4 + 3 + 3$ $2+4+3+2+3+4+3+3$

$=$ $=$ $24$ $24$

Therefore, the sum of the degrees is $24$ $24$ .

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

$(i i)$ $(ii)$ Vertices with $Degree 3 = 4$ $\text(Degree 3)=4$

$(i i i)$ $(iii)$ Sum of Degrees $= 24$ $=24$
Question 3 of 4

3. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Degree of Vertex $A$ $A$ $=$ $=$ (4)
  
  $(i i)$ $(ii)$ Degree of Vertex $B$ $B$ $=$ $=$ (4)
  
  $(i i i)$ $(iii)$ Degree of Vertex $C$ $C$ $=$ $=$ (2)
  
  $(i v)$ $(iv)$ Sum of the Degrees $=$ $=$ (12)
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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 $4$ $4$ edges connected to vertex $A$ $A$ . Therefore, the degree of vertex $A$ $A$ is $4$ $4$ .

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

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

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

$(i i i)$ $(iii)$    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 $2$ $2$ .

$(i v)$ $(iv)$    Sum of the degrees

Get the degrees of all the vertices and add them to get the sum of the degrees.

Sum of Degrees $=$ $=$ $4 + 4 + 2 + 2$ $4+4+2+2$

$=$ $=$ $12$ $12$

Therefore, the sum of the degrees is $12$ $12$ .

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

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

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

$(i v)$ $(iv)$ Sum of Degrees $= 12$ $=12$
Question 4 of 4

4. Question
Using the image below, find the value of the following:
- $(i)$ $(i)$ Degree of Vertex $P$ $P$ $=$ $=$ (4)
  
  $(i i)$ $(ii)$ Degree of Vertex $R$ $R$ $=$ $=$ (4)
  
  $(i i i)$ $(iii)$ Degree of Vertex $S$ $S$ $=$ $=$ (4)
  
  $(i v)$ $(iv)$ Sum of the Degrees $=$ $=$ (20)
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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 $4$ $4$ edges connected to vertex $P$ $P$ . Therefore, the degree of vertex $P$ $P$ is $4$ $4$ .

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

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

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

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

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

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

$(i v)$ $(iv)$    Sum of the degrees

Get the degrees of all the vertices and add them to get the sum of the degrees.

Sum of Degrees $=$ $=$ $4 + 4 + 4 + 4 + 4$ $4+4+4+4+4$

$=$ $=$ $20$ $20$

Therefore, the sum of the degrees is $20$ $20$ .

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

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

$(i i i)$ $(iii)$ Degree of $S = 4$ $S=4$

$(i v)$ $(iv)$ Sum of Degrees $= 20$ $=20$

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2. Question

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Quizzes

Sum of Degrees	$=$ $=$	$4 + 3 + 2 + 4 + 3 + 2$ $4+3+2+4+3+2$
	$=$ $=$	$18$ $18$

Sum of Degrees	$=$ $=$	$2 + 4 + 3 + 2 + 3 + 4 + 3 + 3$ $2+4+3+2+3+4+3+3$
	$=$ $=$	$24$ $24$

Sum of Degrees	$=$ $=$	$4 + 4 + 2 + 2$ $4+4+2+2$
	$=$ $=$	$12$ $12$

Sum of Degrees	$=$ $=$	$4 + 4 + 4 + 4 + 4$ $4+4+4+4+4$
	$=$ $=$	$20$ $20$