(Q). How many regular polygons can be formed by joining the vertices of a 36 sided regular polygon?
Sol:- Since polygon is regular, so all its 36 vertices lie on a circle & are equidistant to its adjacent vertices.
now consider 36 sided regular polygon.
a new regular polygon will be formed from its vertices only when its sides are a factor of 36.
now 36 = 2×2×3×3
∴
Hence desired number of polygon = 12 + 9 + 6 + +4 + 3 + 2 + 1
= 37 Answer