Question

# Arzular polygon with n sides is carried onto itself by a positive rotation about its center that is a multiple of 60, but less than 360°. Which could WOT be the value of n? A 3 B 4 C 5 D. 6

Answer

D. 6

- Q:What is a regular polygon? A:A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
- Q:How do you calculate the interior angle of a regular polygon? A:The formula to calculate the interior angle of a regular polygon is (n-2) x 180 / n, where n is the number of sides.
- Q:What are the possible interior angles for a regular polygon that can be carried onto itself by a positive rotation about its center that is a multiple of 60, but less than 360°? A: The possible interior angles are 60, 120, 180, 240, 300.
- Q:Which could WOT be the value of n? A: If we divide 360 by each of the possible interior angles (60, 120, 180, 240, 300), we get 6, 3, 2, 1.5, 1.2 respectively. Among the given options, n cannot be 4 or 5 because there is no way to divide 360 equally into 4 or 5 parts that are multiples of 60. Therefore, the answer is D. 6.