<image>As shown in the diagram, point O is on the line AD, ∠EOC=90°, and ∠DOB=90°.
(1) If ∠EOD=50°, 

(i) Find the measure of ∠AOC;
(ii) If OM bisects ∠AOC and ON bisects ∠BOC, find the measure of ∠MON;
(2) Rotate ∠EOC around point O for a full turn. Let ∠EOD be α (0°<α<180°). For what value of α does the line OC bisect ∠BOD?