Prove that any 4 vertices of a regular polygon lie on a circle.

All the vertices of a n-sided regular polygon (n ≥ 4) lie on a circle and 4 is a subset of n
=> any 4 vertices of a n-sided regular polygon ( n ≥ 4) lie on a circle.

since each vertical angle satisfies being
right angles,thus,pairs of opposite
vertical angles are supplementary,
satisfies the condition of cyclic
quadrilateral,which passes through
these verticies.