To determine the number of sides of a regular polygon when one interior angle is given as 60 degrees, we can use the formula for finding the measure of an interior angle of a regular polygon:
Interior Angle = (n – 2) * 180° / n
Where n is the number of sides of the polygon.
Plugging 60 degrees into the formula:
60 = (n – 2) * 180 / n
Now, we can multiply both sides by n to eliminate the fraction:
60n = (n – 2) * 180
Expanding the right side:
60n = 180n – 360
Next, we can rearrange the equation to isolate n:
360 = 180n – 60n
So, we have:
360 = 120n
Now divide both sides by 120:
n = 360 / 120
Calculating that gives:
n = 3
Therefore, a regular polygon with an interior angle of 60 degrees must have 3 sides, which is a triangle.