Final answer:
To determine the number of sides for a regular polygon with an interior angle of 60 degrees, the formula for the sum of interior angles is used. The equation (n - 2) × 180 degrees / n = 60 degrees is solved to find that the polygon has 3 sides, which means it is a triangle.
Step-by-step explanation:
To find the number of sides of a regular polygon when one interior angle is 60 degrees, we can use the formula for the sum of interior angles of a polygon which is (n - 2) × 180 degrees, where n is the number of sides. For a regular polygon, each interior angle is the same, and the sum of the interior angles divided by the number of sides will give the measure of one interior angle. So the equation is set up as follows: (n - 2) × 180 degrees / n = 60 degrees. Solving for n gives us:
- n - 2 = 60 degrees × n / 180 degrees
- n - 2 = n/3
- 3n - 6 = n
- 2n = 6
- n = 3
Therefore, the regular polygon with an interior angle of 60 degrees is a triangle, which has 3 sides.