Question

4) A regular pentagon is rotated on a coordinate plane. What angle of rotation would result in a pentagon with vertices at the same coordinates a the vertices of the original pentagon?

Answer 1

The pentagon has a rotational symmetry and the ensures that it can be rotated on a coordinate plane and the result would be a pentagon with vertices at the same coordinates as the vertices of the original pentagon. The angle of rotation would be the smallest angle through which it will be rotated. Since the pentagon has 5 sides and the sum of the angles is 360 degrees,

Angle of roatation = 360/5 = 72 degrees