Systems of measuring angles
The SI unit for measuring angles is Degrees.
Other units for measuring angles are radians and grades.
If the initial ray BC is rotated anti-clockwise to the final position BA, then AB is called the final ray.
Now, an angle is formed between the two rays: the initial ray BC and the final ray BA.
In the above figure, the angle is shown marked with a small curve between the two rays BC and BA.
If the initial ray is rotated anti clockwise a full round, then the measure of the angle so formed is 360 degrees.
The symbol for degree is ‘0‘.
Therefore, 360 degrees is written as 3600.
- One quarter of a full revolution forms an angle whose measure is 90 degrees, written as 900. 900 is the measure of a right angle.
- One half of a full revolution forms an angle whose measure is 180 degrees, written as 1800. 1800 is the measure of a straight line.
Division of Degrees into Minutes and Seconds:
One degree is equal to 60 minutes, i.e. 10 = 60′
The symbol for minute is a small single stroke written at the right top of the number.
One minute equals 60 seconds, i.e. 1′ = 60′′
The symbol for a second is two small strokes written at the right top of the number.
Problems
1. Add 60065′75′′ and 55082′73′′.
Solution:
To find the sum of the given angle measures, write them as below
60065′75′′
55082′73′′
Add seconds to seconds, minutes to minutes and degrees to degrees, just as we add digits of same place values of two numbers.
First add numbers in seconds as below:
75′′ + 73′′ = 148′′ = 120′′ + 28′′′ = 2′ + 28′′ (as 1′ = 60′′)
28′′ remains to be written in the seconds’ place
Carry forward 2′ to the sum of minutes’ numbers as
65′ + 82′ = 147′ + 2′
= 149′ = 120′ + 29′ = 20 + 29′ (10 = 60′)
29′ remains to be written in the minutes’ place
Carry forward 20 to the sum of degrees’ numbers as
600 + 550 = 1150 + 20 = 1170
Therefore, 60065′75′′ + 55082′73′′ = 117029′28′′
Related Topic
Radian
