Quadrilateral WILD is inscribed in circle O.WI is a diameter of circle O.What is the measure of angle D?

Since the quadrilateral is inscribed inside the circle, where the four vertices are on the circle itself, this means that the opposite angles add to 180 degrees.

Angle I and Angle D are opposite angles. They add to 180 degrees

(angle I) + (angle D) = 180
(45 degrees) + (angle D) = 180
(angle D) + 45 = 180
(angle D) + 45 - 45 = 180 - 45 ... subtract 45 from both sides
angle D = 135

The measure of angle D is 135 degrees