To determine the number of sides of a regular polygon based on its interior angle, we can use the formula for the interior angle of a regular polygon, which is given by:
Interior Angle = (n – 2) × 180° / n
Where n is the number of sides of the polygon.
In this case, we know that the interior angle is 120 degrees. Let’s set up the equation:
120 = (n – 2) × 180° / n
To eliminate the fraction, we can multiply both sides by n:
120n = (n – 2) × 180
Now, distribute 180:
120n = 180n – 360
Next, we want to get all terms involving n on one side. Let’s subtract 180n from both sides:
-60n = -360
Now, divide both sides by -60:
n = 6
Therefore, a regular polygon with an interior angle of 120 degrees has 6 sides, which means it is a hexagon.