Let $AB$ and $BC$ be two consecutive sides of a regular polygon with 9 vertices inscribed in a circle of center $O$. Let $M$ be the midpoint of $AB$ and $N$ be the midpoint of the radius perpendicular to $BC$. Find the measure of the angle $\angle OMN$.
Problem
Source: Romanian JBMO TST, Day 4, Problem 16
Tags: trigonometry, geometry, geometry proposed