ABCD is a cyclic quadrilateral with its vertices named in order around the circle. The side AB is produced beyond B to a point E, and the exterior angle CBE measures 75°. What is the measure of angle ADC?

The exterior angle of a cyclic quadrilateral equals the interior angle at the opposite vertex. Angle CBE = 180° − angle ABC, and angle ADC = 180° − angle ABC because opposite angles of a cyclic quadrilateral are supplementary. Hence angle ADC = angle CBE = 75°. Choosing 105° is the trap of taking the supplement instead of the angle itself.