Perhaps you have seen a team of surveyors decked out in their orange vests along the roadside viewing the land through what looks like a telescope. That telescope is actually a theodolite, a tool used to measure angles that is not exclusive to surveying crews. Since the 17th century, theodolites have been the primary tool used in geodetic surveys. The theodolite employs a Vernier scale, which, with a little practice, can accurately measure angles to the minute.
Learn angle basics. Before you can understand the Vernier scale on a theodolite, you must know how angles are broken up. A full circle consists of 360 degrees. Each degree (or 1/360 of a circle) can be divided into 60 minutes.
Look at the Vernier scale on your theodolite or refer to the Vernier model in the References. The outer circle on the scale is fixed, while the inner scale is rotated as the scope of the theodolite is rotated. Each interval marking signifies 30 minutes, or 1/2 of a degree.
Study the outer scale. The top number tells you what the angle is to the right. If you were to draw an arc to the right from the theodolite to the object being surveyed the top number would give you the angle measure of that arc. The complementary arc to the left is read using the bottom number. Adding the angle to the right and the angle to the left will always equal 360 degrees. Note that the number on top decreases from left to right while the bottom number decreases.
Find the "0" mark on the inner (movable) scale. This is your baseline. Wherever the 0 falls in relation to the outer scale is your degree measure. If the 0 mark falls right on the 130 (top) 230 (bottom) line, then your angle right is 130 degrees and your angle left is 230 degrees.
Count the minutes. If the 0 mark of the inner scale falls directly on a mark on the outer scale, your degree measure exact. If, however, the 0 mark falls in between two interval markings, then your degree measure is not exact. Moving toward the right of the 0 mark, count the interval markings until one lines up directly with the interval mark beneath it. This is the minutes of your angle.