Math Counts 4

$\binom{17}{2}=136 -17=119$

Every two points define an edge; therefore, we have 136 edges minus the 17 sides of the polygon we get 119 diagonals.

Every diagonal is defined by its two endpoints, so we have to count the number of ways to choose 2 out of 17 points, with the restriction that we can't choose the same point twice and also no two adjacent points.

There are $17$ possibilities for the first point and $17-3 = 14$ for the second point, but with that we're counting every diagonal twice, so we have to divide by $2$ . In total, there are $\frac {17 \cdot 14} 2 = \boxed{119}$ diagonals.

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