Question

Through which angle measures can a regular decagon be rotated so that it maps onto itself?

A) 10°
B) 100°
C) 180°
D) 396°

Answer 1

A regular decagon can be rotated through an angle of 10° in order to map onto itself.

Step-by-step explanation:

A regular decagon is a polygon with ten sides of equal length and ten angles of equal measure. In order for the decagon to map onto itself after rotation, the angle of rotation needs to be a factor of 360 degrees, because a full rotation is 360 degrees. The angles that are factors of 360 degrees are 10 degrees (36 times), 20 degrees (18 times), 30 degrees (12 times), 40 degrees (9 times), 60 degrees (6 times), 120 degrees (3 times), and 180 degrees (2 times). Therefore, the correct answer is A) 10°.