ABCD is a quadrilateral inscribed in a circle, with its vertices in order, and the side AB is parallel to the side DC. If angle A measures 65°, what is the measure of angle C?

Opposite angles of a cyclic quadrilateral are supplementary, so angle C = 180° − 65° = 115°. This is consistent with AB ∥ DC: taking AD as a transversal makes angles A and D co-interior, so angle D = 115°, and then angle B = 180° − 115° = 65°. The four angles 65°, 65°, 115° and 115° do add to 360°.