ABCD is a cyclic quadrilateral, with its vertices named in order around the circle, and the side AD is a diameter of that circle. If angle ABC = 130°, what is the measure of angle CAD?

Opposite angles of a cyclic quadrilateral are supplementary, so angle ADC = 180° − 130° = 50°. Because AD is a diameter, the angle it subtends at C is a right angle, so angle ACD = 90°. In triangle ACD, angle CAD = 180° − 90° − 50° = 40°. Answering 50° stops one step early, at angle ADC.