Question

A regular polygon is rotated 20 degrees about its center, carrying the polygon onto itself. How many sides does the polygon have?

1) 20

2) 8

3) 36

4) 10

Answer 1

36

Explanation:

Given that :

Rotation about polygon's center = 20°

To carry the polygon onto itself Angle of rotation is obtained by :

360° / n

Where n is the number of sides in the polygon :

360° / n = 20°

360° = 20 * n

360 = 20n

n = 360 / 20

n = 18

Hence, the polygon has 18 sides or a multiple of 18