When you are given the diversion, you should be told "When you are ready, take me to....". This will normally be given to you by the Examiner when there is a hugely obvious feature from which to set off clearly nearby. Lots of easy ways to measure angles, but I had checklists produced with a laminated back on which there was a 1:500 000 scale on one edge and lots of blank area on which to write. Use a chinagraph pencil, pop the checklist from where you're going to divert from to the diversion point on the map, draw the track line - measure the distance and scribble it on the blank area. Now wiggle the checklist across to the nearest convenient VOR rose and measure the track by using the checklist as a parallel rule. You now have track and distance - now apply Mental Dead Reckoning, jot down the heading and time, turn carefully onto the correct heading, check the DI and hack the watch. Update your estimate with map-to-ground work and there you have it!