For an inscribed quadrilateral, opposite angles add up to 180 degrees. In this case, if we are looking for the measure of angle D, we can use the fact that angles I & D add up to 180 degrees. Since angle I = 117:
117 + D = 180
D = 63 degrees
Time it by the number before hand and you get 8 then 16 then 32 . Think about it it works and it’s a consistent continental