SOLUTION: how many diagonals does a polygon have if its angle sum is 1080 degrees ?

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Question 471072: how many diagonals does a polygon have if its angle sum is 1080 degrees ?
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
First find the number of sides of the polygon:
180%28n-2%29+=+1080
n-2+=+6
n+=+8
Next find the number of diagonals in a octagon:
There are 8 vertices and from each vertex 5 diagonals can be drawn.
**you can't draw a diagonal to an adjacent vertex or to itself**
Also each diagonal is shared by 2 vertices
This leads to the general formula: %28n%28n-3%29%29%2F2
diagonals = %288%29%285%29%2F2+=+20