It's a method of measuring angles other than the more mainstream, simpler format.
First you write the degree with the degree symbol, then you write the amount of minutes, which are 1/60 of a degree, and finally you write the seconds, which are 1/60 of minutes and therefore 1/3600 of a degree. It can be tricky to convert, but you should be able to do it back and forth with a graphing calculator.
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Angles are measured by degrees. Fractions of degrees are measured in minutes and seconds.
There are 360 degrees in a full circle. 60 minutes in 1 degree 60 seconds in 1 minute Therefore: 360 x 60 x 60 = 1,296,000 seconds
An Angle and its complement add to 90o, so the complement of 25o19'12'' is: 90o - 25o19'12" = 64o40'48" as there are 60 seconds to every minute and 60 minutes to every degree.
40 minutes is 0.667 degrees.