The degree is a unit of measurement of angles and is represented by the symbol °.
In degrees, we split up one complete rotation into 360 equal parts and each part is one degree, denoted by 1°. Thus, 1° is 1/360 of one complete rotation.
To measure a fraction of an angle and also for accuracy of measurement of angles, minutes and seconds are introduced. One minute (1') corresponds to 1/60 of a degree and in turn a second (1'') corresponds to 1/60 of a minute (or) 1/3600 of a degree.
We shall classify a pair of angles in the following way for better understanding and usages.
(i) Two angles that have the exact same measure are called congruent angles.
(ii) Two angles that have their measures adding to 90° are called complementary angles.
(iii) Two angles that have their measures adding to 180° are called supplementary angles.
(iv) Two angles between 0° and 360° are conjugate if their sum equals 360°.
(i) The concept of degrees, minutes and seconds, is analogous to the system of time measurement where we think of a degree representing one hour.
(ii) Observe that
59.0854° = 59° + 0.0854°
0.0854° = 0.0854° ⋅ (60'/1°) = 5.124'
5.124' = 5' + 0.124'
0.124' = 0.124' ⋅ (60"/1') = 7.44"
Thus,
59.0854° = 59°5'7.44"
(iii) Also notice that
34°51'35" = 34.8597°
and
90° - 36°18'47" = 53°41'13"
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