What is the number of sides of a regular polygon for which the number of diagonals is or ?

Source: NCTM Mathematics Teacher 2006

**SOLUTION**

The number of diagonals of a convex polygon of vertices (or sides) is given by . Please refer to post titled “Convex Polygon” posted on 6/18/2011 for details.

Case 1: diagonals

Let’s try a few numbers

The polygon has sides.

Case 2: diagonals

Continuing where we left off above we get

Clearly, there is no polygon that has diagonals.

**Answer**:

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