How many sides does a regular polygon have if each interior angle measures $60°$?

• A. $6$
• B. $5$
• C. $3$
• D. $4$

Answer: (C)

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: \$60^\circ = \frac{(n-2) \times 180^\circ}{n}$.
3. Multiply both sides of the equation by \(n\) to eliminate the denominator: \$60n = (n-2) \times 180$.
4. Expand the right side: \$60n = 180n - 360$.
5. Rearrange the equation to isolate \(n\) and solve for it: \$180n - 60n = 360\(, then simplify to find \)n$.