Let A B C be a triangle with circumcenter O. Additionally, \angle B A C=20^{\circ} and \angle B C A=70^{\circ}. Let D, E be points on side A C such that B O bisects \angle A B D and B E bisects \angle C B D. If P and Q are points on line B C such that D P and E Q are perpendicular to A C, what is \angle P A Q?