ABCD is a rectangle whose diagonals AC and BD meet at O. If angle AOB = 110°, what is the measure of angle ODA?

The diagonals of a rectangle are equal and bisect each other, so OA = OB = OC = OD. Since B, O and D are collinear, angle AOD = 180° − 110° = 70°. Triangle AOD has OA = OD, so angle ODA = angle OAD = (180° − 70°)/2 = 55°. The trap 35° is angle OAB, which comes from working inside triangle AOB instead of triangle AOD.