How many sides does a regular polygon have if each interior angle measures $160°$?

• A. $15$
• B. $18$
• C. $9$
• D. $12$

Answer: (B)

Verified step by step guidance

1. Recall the formula for the measure of each interior angle of a regular polygon with n sides: \(\text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}\).
2. Set the given interior angle equal to the formula: \$160^\circ = \frac{(n-2) \times 180^\circ}{n}$.
3. Multiply both sides of the equation by n to eliminate the denominator: \$160n = (n-2) \times 180$.
4. Expand the right side: \$160n = 180n - 360$.
5. Rearrange the equation to isolate n and solve for it: \$180n - 160n = 360\(, which simplifies to \)20n = 360\(, then \)n = \frac{360}{20}$.