Question

If any line of symmetry in a regular polygon connects midpoint of two of its sides, then which of the following may be the number of sides of that polygon?

• A. 1000
• B. 1003
• C. 1006
• D. 1009

Answer 1

Answer: (A), (C)

The correct options are
A

1000

C

1006

Only in regular polygons with even number of sides, we can have lines of symmetries which join midpoints of two sides. In regular polygons having odd number of sides, this is not possible. Every line of symmetry joins the vertex to the midpoint of the opposite side.

Since, the regular polygon should have even number of sides, only options A and C can be the possible number of sides.