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How many sides does a regular polygon have if each interior angle measures ?
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1
Recall the formula for the measure of each interior angle of a regular polygon with \(n\) sides: \(\text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}\).
Set the given interior angle equal to the formula: \(60^\circ = \frac{(n-2) \times 180^\circ}{n}\).
Multiply both sides of the equation by \(n\) to eliminate the denominator: \(60n = (n-2) \times 180\).
Expand the right side: \(60n = 180n - 360\).
Rearrange the equation to isolate \(n\) and solve for it: \(180n - 60n = 360\), then simplify to find \(n\).