In a certain polygon, if one angle measures 120 degrees and the polygon is regul

In a certain polygon, if one angle measures 120 degrees and the polygon is regular, how many sides does it have?

In a certain polygon, if one angle measures 120 degrees and the polygon is regular, how many sides does it have?

Step 1: Understand that a regular polygon has all sides and angles equal.
Step 2: Know the formula to find the measure of each interior angle of a regular polygon: (n-2) * 180 / n, where n is the number of sides.
Step 3: Set the formula equal to 120 degrees because we want to find out how many sides correspond to that angle: (n-2) * 180 / n = 120.
Step 4: Multiply both sides of the equation by n to eliminate the fraction: (n-2) * 180 = 120n.
Step 5: Distribute 180 on the left side: 180n - 360 = 120n.
Step 6: Move all terms involving n to one side: 180n - 120n = 360.
Step 7: Simplify the equation: 60n = 360.
Step 8: Divide both sides by 60 to solve for n: n = 360 / 60.
Step 9: Calculate the result: n = 6.
Step 10: Conclude that the polygon is a hexagon because it has 6 sides.

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