To find the number of sides of a regular polygon based on its interior angle, we can use the formula for the measures of the interior angles of a polygon:
Interior Angle = (n – 2) × 180° / n
Where n is the number of sides of the polygon.
In your case, you mentioned that one interior angle measures 60 degrees. By setting the above formula equal to 60 degrees, we get:
60 = (n – 2) × 180 / n
Now, we can multiply both sides by n to eliminate the fraction:
60n = (n – 2) × 180
Next, expand the equation:
60n = 180n – 360
Now, let’s rearrange the equation to solve for n:
360 = 180n – 60n
This simplifies to:
360 = 120n
Now, divide both sides by 120:
n = 360 / 120
Thus, n = 3.
Therefore, a regular polygon with an interior angle of 60 degrees has 3 sides, meaning it is a regular triangle.