How many DIAGONALS does a regular DECAGON (10-sided polygon) have?

1. A polygon with $n$ vertices has $\binom{n}{2}$ ways to connect two vertices — these are all the line segments. 2. Of these, $n$ are the SIDES of the polygon (consecutive vertex pairs). 3. The rest are DIAGONALS: $\binom{n}{2} - n$. 4. For a decagon ($n = 10$): diagonals = $\binom{10}{2} - 10 = 45 - 10 = 35$. 5. Useful formula: number of diagonals of an $n$-gon = $\dfrac{n(n-3)}{2}$. Check: $10 \cdot 7 / 2 = 35$ ✓. 6. Option A is just $n$ (the sides count). Option B is half by mistake. Option D is $\binom{10}{2}$ — forgot to subtract sides. _Source: syllabus Mathematics, Ch 6, §6.4 + Geometry applications, p. 12._