If you don't have the item that goes into the counter sink hole to measure you may make in impression of the cavity angle and place that clay or aluminum foil gob squarely onto an optical comparator to enlarge the profile. Measure the profile angle on the screen with a machinists protractor etc.
For location and sizing of holes or features (geotolerancing) I have used rubbings made with lead pencil and paper. Sometimes it helps to put the pencil lead on your finger to rub on the paper in hard to access areas. Don't let the paper slip. Keep the paper referenced or "indexed" from a major feature. Rubbings are less obtrusive and far more precise than using a tiny camera ( like the old 8mm Minox, or Yashica etc).