



 
Hi Julie, Lets start with a definition: a diagonal is a line segment which joins two nonadjacent vertices in a polygon. Now let's consider some simpler shapes than a 12sided figure.
I could continue, but perhaps you have noticed that regardless of how many sides the polygon has, once I choose a vertex, there are three vertices to which I can not connect to make a diagonal (the one I chose, and the two adjacent vertices). Therefore, in general, for any polygon of n sides, there will be (n  3) diagonals that can be drawn from one vertex. Hope this helps,  


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