## Systems of measuring angles

The SI unit for measuring angles is Degrees. 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

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′′

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