<p>Find the number of diagonals in a quindecagon (15-sided polygon).</p>
Step-by-Step Solution
Key Concept: Diagonals are all line segments between vertices except the sides; use combination to count total line segments and subtract the number of sides.
<p><strong>Step 1:</strong> A quindecagon has 15 sides, so 15 vertices.</p><p><strong>Step 2:</strong> Total number of line segments joining any two vertices = <span class="math">\binom{15}{2} = \frac{15 \times 14}{2} = 105\</span></p><p><strong>Step 3:</strong> Number of sides = 15</p><p><strong>Step 4:</strong> Number of diagonals = Total line segments - Number of sides</p><p><span class="math">= 105 - 15 = 90\</span></p><p>∴ The number of diagonals is <strong>90</strong>.</p>
Correct Answer: 90