This problem might look easy to solve just by calculating angles, but try switching strategy, and use the Theorem of Pythagoras to determine the sides of triangle BPQ. One way is to first determine the altitude of triangle CDI from I, from which you can get AP, etc. Alternatively, from the step before, use trigonometry to show that ∠ABP = 15o, etc. For the case outside, make an accurate construction and look for and prove a connection between the inside and outside cases. (Click here for an Accurate construction showing the equilateral triangles on the outside).