If the sum of the interior angles of a polygon is $1080°$, how many sides does the polygon have?

• A. $7$
• B. $6$
• C. $10$
• D. $8$

Answer: (D)

Verified step by step guidance

1. Recall the formula for the sum of the interior angles of a polygon with \( n \) sides: \[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
2. Set the given sum of interior angles equal to the formula: \[ 1080^\circ = (n - 2) \times 180^\circ \]
3. Divide both sides of the equation by \( 180^\circ \) to isolate \( n - 2 \): \[ \frac{1080^\circ}{180^\circ} = n - 2 \]
4. Simplify the left side to find \( n - 2 \): \[ 6 = n - 2 \]
5. Add 2 to both sides to solve for \( n \): \[ n = 6 + 2 \]