Question

What is the least angle by which a regular 60-gon (60 sides) can be rotated so that it maps onto itself? A) 36 B) 18 C) 12 D) 6

Answer 1

Answer:

Correct choice is D

Step-by-step explanation:

Consider regular 60 sided polygon (regular means all sides are of equal length). Connect the center of this polygon with each polygon's vertex. You get 60 equal isosceles triangles with base that is polygon's side. The measure of the angle opposite to the base is

$\dfrac{360^{\circ}}{60}=6^{\circ}.$

Rotating the polygon by 6° over the center, each such triangle will map onto the previous triangle. Thus, the least angle by which a regular 60-gon can be rotated so that it maps onto itself is 6°.