Question

A regular polygon has 15 sides. Which is a possible angle of rotational symmetry for the figure? 12° 45° 72° 90°

Answer 1

72

Explanation:

took the test and 72 was correct

Answer 2

Option (3). 72°

Explanation:

Angle of rotational symmetry = Central angle of a polygon

That means when we rotate the regular polygon by a central angle, polygon overlaps itself.

Central angle of a polygon with n sides =
`(360)/(n)`

Where n = number of sides of the polygon

Therefore, central angle of a polygon with 15 sides =
`(360)/(15)`

= 24°

Central angle tells us that after every 24° of rotation, polygon overlaps itself.

Angle of rotational symmetry may be 48°, 72°, 96°.....

Therefore, Option (3) is the possible angle of rotational symmetry.