Question

Which of the following cannot be the angles of rotational symmetry for a regular polygon with odd number of sides?

• A. ${40}^{\circ }$
• B. ${72}^{\circ }$
• C. ${180}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is C

${180}^{\circ }$

This problem may seem difficult at first sight but it is pretty simple. Just think of it like this. In every regular polygon having ‘n’ sides, if you join the center with the vertices, the central angle will be divided into ‘n’ parts, each part equal to 360°/n.

Also, if you rotate the polygon for 360°/n or any multiple of that, it will reach its original position. For example, in a regular nonagon (9 sides), the angle of rotation can be either 360°/9, i.e. 40°, or multiples of 40°.