SOLUTION: Consider a polygon with n sides.a)Find a mathematical equation that relates the number of diagonals in the polygon to the number of sides.b)Use your equation to find, 1)The number

Question 478757: Consider a polygon with n sides.a)Find a mathematical equation that relates the number of diagonals in the polygon to the number of sides.b)Use your equation to find, 1)The number of diagonals if the polygon has 17 sides.2)The number of sides if the polygon has 119 diagonals.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula for determining the number of diagonals in a polygon is:

the derivation of this formula is as follows:
each vertex in a polygon can connect to n-3 other vertices.
the only ones it can't connect to are itself and the vertices that are adjacent to it.
if you have a pentagon, there are 5 vertices. each one of these can connect to 2 other vertices for a total of 10 diagonals. each diagonal connects between 2 vertices, so the number of diagonals has to be divided by 2 in order to avoid double counting.
the number of diagonals in the pentagon is therefore (5 * 2) / 2 = 5
a picture of your pentagon is shown below.
explanations are below the picture.
$$$$

point A connects to C and D
point B connects to D and E
point C connects to E and A
point D connects to A and B
point E connects to B and C
the diagonals formed are:
AC
AD
BD
BE
CE
CA
DA
DB
EB
EC
that's a total of 10.
however,
AC and CA are the same diagonal
AD and DA are the same diagonal
BD and DB are the same diagonal
BE and EB are the same diagonal
CE and EC are the same diagonal
cross off the duplicates and you're left with 5.
that's why the formula for determining the number of diagonals is:
(n*(n-3))/2

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