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 360^{0}.

- One quarter of a full revolution forms an angle whose measure is 90 degrees, written as 90
^{0}. 90^{0}is the measure of a right angle. - One half of a full revolution forms an angle whose measure is 180 degrees, written as 180
^{0}. 180^{0}is the measure of a straight line.

**Division of Degrees into Minutes and Seconds:**

One degree is equal to 60 minutes, i.e. 1^{0} = 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 60^{0}65′75′′ and 55^{0}82′73′′.

**Solution: **

To find the sum of the given angle measures, write them as below

**60 ^{0}65′75′′**

**55 ^{0}82′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′ = 2^{0} + 29′ (1^{0} = 60′)

29′ remains to be written in the minutes’ place

Carry forward **2 ^{0} **to the sum of degrees’ numbers as

**60 ^{0} + 55^{0} = 115^{0} + 2^{0} = 117^{0}**

Therefore, 60^{0}65′75′′ + 55082′73′′ = 117^{0}29′28′′

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