How many sides does a polygon have if the sum of its interior angles is $1440°$?

• A. $12$
• B. $8$
• C. $9$
• D. $10$

Answer: (D)

Verified step by step guidance

1. Recall the formula for the sum of the interior angles of a polygon: \(\text{Sum of interior angles} = (n - 2) \times 180^\circ\), where \(n\) is the number of sides of the polygon.
2. Set up the equation using the given sum of interior angles: \((n - 2) \times 180^\circ = 1440^\circ\).
3. Divide both sides of the equation by \$180^\circ\( to isolate \)(n - 2)\(: \)n - 2 = \frac{1440}{180}$.
4. Simplify the right side of the equation to find the value of \((n - 2)\).
5. Add 2 to both sides to solve for \(n\), the number of sides of the polygon.