Problem

A regular polygon's interior angles tell you how many sides it has—use the formula that each interior angle equals $\frac{(n-2) \cdot 180°}{n}$. Once you know $n$, the number of diagonals follows from counting all possible line segments between vertices, minus the sides themselves. The key insight is that every pair of vertices can connect, but only $n$ of those pairs form the edges.

A regular polygon's interior angles tell you how many sides it has—use the formula that each interior angle equals $\frac{(n-2) \cdot 180°}{n}$. Once you know $n$, the number of diagonals follows from counting all possible line segments between vertices, minus the sides themselves. The key insight is that every pair of vertices can connect, but only $n$ of those pairs form the edges.