SOLUTION: How many diagonals does a 30-sided polygon have? How do you find a formula to solve this?

Question 54170: How many diagonals does a 30-sided polygon have?
How do you find a formula to solve this?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How many diagonals does a 30-sided polygon have?
How do you find a formula to solve this?
----------
If you know something about combinations the number
of pairs of points is 30C2=[30)(29)/2]=15(29)=435
But 30 of those pairs form the sides of the polygon
So the # of diagonals is 435-30=405
Try this on smaller polygons.
For example how about a pentagon
5C2-5 = [5*4/2]-5 sides = 10-5=5 diagonals
A formula would look like nC2 - n = [(n)(n-1)/2 -n] or (n^2-3n)/2
Cheers,
Stan H.
RELATED QUESTIONS
How many diagonals does a 101-sided convex polygon have than a 100-sided convex... (answered by MathLover1)

A regular polygon has 6 times as many diagonals as sides. How many sides does this... (answered by MathTherapy)

how many diagonals does a polygon with 32 sides have? and how do you figure out this type (answered by stanbon)

How many diagonals does a polygon with 20 sides have? (answered by josgarithmetic,math_tutor2020)

If the number of diagonals of a polygon is 170, how many sides does it have? Explain how... (answered by solver91311)

Each exterior angle of a polygon measures 7.5 degrees. How many diagonals does the... (answered by solver91311)

An n-sided polygon has (n(n - 3))/2 diagonals. a How many sides has a polygon with 665 (answered by MathLover1,htmentor)

How Many Diagonals Can Be Drawn From One Vertex Of A 12 Sided Polygon? Can you please... (answered by stanbon)

How many diagonals can be drawn from one vertex of a 12 sided... (answered by glitzgirl_14)