In geometry, an angle. is measured in degrees, where a full circle is 360 degrees. A small angle might be around 30 degrees. Usually, when a finer measure is needed we just add decimal places to the degrees. For example 45.12°
The small circle after the number means "degrees". So the above would be pronounced "forty five point one two degrees".
When measuring things like latitude and longitude, each degree is divided into minutes and seconds. The degree is divided in to 60 minutes. For even finer measurements the minute is divided again into 60 seconds, However this last measure is so small, it only used where angles are subtended over extreme distances such as astronomical measurements, and measuring latitude and longitude.
These minutes and seconds have (confusingly) nothing to do with time. They are just smaller and smaller parts of a degree.
See also Degrees - Minutes - Seconds calculator for a calculator that can add and subract angles in this form.
|Degrees||With a small circle after the number.
|Minutes||With a small dash after the number.
Example 34° 21'
|"34 degrees, 21 minutes"|
|Seconds||With two small dashes.
Example 32° 34' 44''
|"32 degrees, 34 minutes, 44 seconds"|
In the figure above, adjust the point R so the line crosses the point marked 315°. Starting at Q and going counter-clockwise we see the measure is 315°. But if we were to go clockwise from Q it would be 45° (360-315). Which is correct?
They both are, but by convention the smaller one is assumed. That is why the angle at the center shows 45° under these circumstances. The larger measure (315°) is called the reflex angle RPQ.
You should especially be able to estimate angles close to the red ones in the figure above, since they appear frequently in geometry.