Let n denote the largest odd integer for which the internal angles of a regular n-sided polygon, each measures x degrees, where x is an integer. Find the number of diagonals in the polygon of side n.

Engineering

Mathematics

Fundamental Principal of Counting

Question

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ach internal angle $= θ = 180^{\circ} - \frac{360^{\circ}}{n}$
∴ largest odd divisor of 360° is 45 ⇒ n = 45
Hence number of diagonals = $\frac{45 (45 - 3)}{2} = \frac{45 \times 42}{2}$ = 45 × 21 = 945

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