SOLUTION: HOW MANY DIAGONALS CAN BE DRAWN FROM ONE VERTEX OF A REGULAR OCTAGON?

Question 96363: HOW MANY DIAGONALS CAN BE DRAWN FROM ONE VERTEX OF A REGULAR OCTAGON?
Found 2 solutions by scott8148, bucky:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
a regular octagon has 8 vertices; so from one vertex, lines can be drawn to the other 7 vertices

the lines to the two adjacent vertices are sides of the octagon ... the other 5 lines are diagonals
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Although it is true that from any vertex of a regular octagon lines can be drawn to 7 other
vertices, those lines are NOT diagonals.
.
In a regular octagon, from a vertex you can only draw 5 diagonals. A line from a vertex to the next
adjacent vertex on either side is not a diagonal.
.
Let's use something you are familiar with. If you are given a square (which has four
sides and is a quadrilateral), how many diagonals can you draw from one corner? The answer
is 1 diagonal from that corner, not 4 - 1 = 3. From one vertex in a square the only
diagonal you can draw is from that vertex to the vertex in the opposite corner.
.
In fact, for any regular geometric figure the answer to this question is N - 3 where N is
the number of sides of the given figure.
.
So, from one vertex in:
.
a regular triangle you can draw 3 - 3 = 0 diagonals
a regular quadrilateral you can draw 4 - 3 = 1 diagonal
a regular pentagon you can draw 5 - 3 = 2 diagonals
a regular hexagon you can draw 6 - 3 = 3 diagonals
a regular heptagon you can draw 7 - 3 = 4 diagonals
a regular octagon you can 8 - 3 = 5 diagonals
and so on
.
Hope this helps you to see why the answer to your problem is 5 diagonals, not 7.
.

RELATED QUESTIONS
How many diagonals can be drawn from one vertex of a 12 sided... (answered by glitzgirl_14)
For each polygon, how many diagonals can be drawn from one vertex? How many different... (answered by solver91311)
How Many Diagonals Can Be Drawn From One Vertex Of A 12 Sided Polygon? Can you please... (answered by stanbon)
How many triangles are formed by the diagonals from one vertex of a regular octagon? I... (answered by jim_thompson5910)
how many diagonals can be drawn from each vertex of a... (answered by solver91311)
How many diagonals can be drawn from a vertex of an n-gon? (answered by stanbon)
How many interior angles does a undecagon have? How many diagonals can be drawn from... (answered by stanbon)
How many diagonals could be drawn from one vertex for a... (answered by stanbon,solver91311,lizard)