In the courtyard of Eastside HS, there is a gazebo in the shape of a 15 sided regular polygon. To
decorate for homecoming, Ms. Jones will drape streamers across the interior of the gazebo. Each
streamer represents a diagonal of the polygon. How many diagonals does a regular 15-gon have?

 90

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Work Shown:

n = number of vertices = 15

d = number of diagonals

So there are 90 diagonals for this 15-gon.

The numerator n(n-3) is from the fact that there are n vertices, and for each vertex, there are n-3 points to connect to that will form a diagonal. Why n-3? The 3 comes from the fact that you cannot select the current point, or either neighboring point (on either side). So we ignore 3 points when forming diagonals for any vertex. That's why n drops to n-3.

The 2 in the denominator is to correct for double-counting. A diagonal like AB is the same as BA. The order does not matter when it comes to naming a segment.

step-by-step explanation: