Degrees 3
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Question 1 of 3
1. Question
Using the image below, find the value of the following:
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`(i)` Degree of Vertex `G``=` (6)`(ii)` Degree of Vertex `C``=` (3)`(iii)` Degree of Vertex `F``=` (2)`(iv)` Total number of Edges `=` (11)
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A degree is the number of edges that connects to a vertex.`(i)` Degrees of Vertex `G`Count the edges connecting to vertex `G`.
There are `6` edges connected to vertex `G`. Therefore, the degree of vertex `G` is `6`.`(ii)` Degrees of Vertex `C`Count the edges connecting to vertex `C`.
There are `3` edges connected to vertex `C`. Therefore, the degree of vertex `C` is `3`.`(iii)` Degrees of Vertex `F`Count the edges connecting to vertex `F`.
There are `2` edges connected to vertex `F`. Therefore, the degree of vertex `F` is `2`.`(iv)` Total number of EdgesGet the number of edges, or the lines connecting the vertices.
There are `11` lines connecting the vertices. Therefore, the total number of edges is `11`.`(i)` Degree of `G=6``(ii)` Degree of `C=3``(iii)` Degree of `F=2``(iv)` Total number of Edges `=11` -
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Question 2 of 3
2. Question
Using the image below, find the value of the following:
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`(i)` Number of Vertices `=` (9)`(ii)` Degree of Edges `=` (13)`(iii)` Number of Odd Vertices `=` (6)`(iv)` Number of Even Vertices `=` (3)
Hint
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A degree is the number of edges that connects to a vertex.`(i)` Number of VerticesCount the vertices or points in the figure.
The figure has `9` points in it. Therefore, the total number of vertices is `9`.`(ii)` Number of EdgesGet the number of edges, or the lines connecting the vertices.
There are `13` lines connecting the vertices. Therefore, the total number of edges is `13`.`(iii)` Number of Odd VerticesFind the degree of all the vertices and count the vertices with an odd number of degrees.
Vertices `A`, `B`, `D`, `F`, `H`, and `I` all have odd number of degrees. Therefore, the number of odd vertices is `6`.`(iv)` Number of Even DegreesFind the degree of all the vertices and count the vertices with an even number of degrees.Vertices `C`, `E`, and `G` all have even number of degrees. Therefore, the number of even vertices is `3`.`(i)` Number of Vertices `=9``(ii)` Number of Edges `=13``(iii)` Number of Odd Vertices `=6``(iv)` Number of Even Vertices `=3` -
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Question 3 of 3
3. Question
Using the image below, find the value of the following:
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`(i)` Degree of Vertex `A``=` (5)`(ii)` Degree of Vertex `C``=` (4)`(iii)` Number of Odd Vertices `=` (4)`(iv)` Total Number of Edges `=` (10)
Hint
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Correct!
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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`.
Notice that there is a loop connected to vertex `A`.
A loop consists of `2` edges. Therefore, there are a total of `5` edges connected to vertex `A`. Therefore, the degree of vertex `A` is `5`.`(ii)` Degrees of Vertex `C`Count the edges connecting to vertex `C`.
There are `4` edges connected to vertex `C`. Therefore, the degree of vertex `C` is `4`.`(iii)` Number of Odd VerticesFind the degree of all the vertices and count the vertices with an odd number of degrees.
Vertices `A`, `B`, `D`, and `E` all have odd number of degrees. Therefore, the number of odd vertices is `4`.`(iv)` Total number of EdgesGet the number of edges, or the lines connecting the vertices.
There are `10` lines connecting the vertices. Therefore, the total number of edges is `10`.`(i)` Degree of `A=5``(ii)` Degree of `A=4``(iii)` Number of Odd Vertices `=4``(iv)` Total number of Edges `=10` -
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