3. Let $N$ be a regular nonagon, $O$ the center of its circumscribed circle, $P Q$ and $Q R$ two consecutive sides of $N$, $A$ the midpoint of $P Q$, and $B$ the midpoint of the radius perpendicular to $Q R$. Find the angle between $A O$ and $A B$.
3. Let $C$ be the intersection of the radius perpendicular to $Q R$ and the circumcircle of $N$, as shown in Figure 12-15. Since $\angle P O Q=40^{\circ}, \angle Q O R=40^{\circ}$, and $O C$ bisects $\angle Q O R$, it follows that $\angle P O C=60^{\circ}$. Also, since $O P = O C$, $\triangle P O C$ is an equilateral triangle, and $P B \perp O C$. Furthermore, $\angle P A O=90^{\circ}$, so points $A, B, O$, and $P$ are concyclic, thus $\angle B A O=\angle B P O=30^{\circ}$.