Reading a Vernier scale protractor

[Jeff the Green]

In which I once again demonstrate my inability to understand anything related to the physical sciences.

I'm trying to write a document explaining how to measure the angle of repose using angle finders as in the image below, which I basically get. It's reading the Vernier scale I don't get. The angle is obviously between 25° and 30°, but I don't understand how you can get more precise from that. Help, please?

http://oi62.tinypic.com/255mn2v.jpg

[crayzz]

If I'm reading that right, the measurement is 27.67o, or 27o + 40 minutes.

You read the scale by looking at the 0 point on the vernier scale. If the 0 lines up perfectly with the large scale, then that's your value. If it doesn't, like in this case, then you find out where it does line up. Here, the 0 is between 27o and 28o. Looking along the vernier scale, both scales line up best at 40 minutes along the positive side, and 20 minutes along the negative side. So our angle is 27o + 40 minutes, or 28o - 20 minutes.

60 minutes = 1o. Presumably a hold over from Mesopotamia, who, in ancient times, counted in base 60 (which is also why there's 60 seconds to a minute, and 60 minutes to an hour; never underestimate the power if being the first to set the standard.) Anyways, 40 minutes is (40/60)o, or 0.67. 20 minutes is (20/60)o, or 0.33. So we read 27o + 0.67o, or 28o - 0.33o, in each case getting 27.67o. You should only get one answer here; if you ever get two different answers, there's probably something wrong.

EDITED