How Do You Add Up Degrees?

Adding up degrees, particularly when they are expressed with minutes and seconds, involves a straightforward process of organizing and summing each unit separately. The method is similar to adding time.

To add angles expressed in degrees (°), minutes ('), and seconds ("), you line up the degrees, minutes, and seconds and add each column separately.

Step-by-Step Guide to Adding Degrees, Minutes, and Seconds

Based on the method described in the reference, the fundamental steps are as follows:

1. Line Up: Arrange the angles vertically, ensuring that the degrees, minutes, and seconds are aligned in their respective columns.
2. Add Separately: Add the numbers in each column (seconds, minutes, and degrees) independently.

As the reference states, "So you sort of line up your degrees and your minutes. And your seconds. And just add each separately." For example, when adding an angle like 32° 29 minutes and 38 seconds to another angle, you would align its components under the corresponding columns of the second angle.

After adding each column, you often need to perform conversions because minutes and seconds are based on a base-60 system (60 seconds in a minute, 60 minutes in a degree).

Handling the Sums (Carrying Over)

Once you have the initial sums for seconds, minutes, and degrees:

• Seconds: If the sum of seconds is 60 or greater, divide the total seconds by 60. The remainder is the final seconds value, and the quotient is carried over and added to the minutes column.
• Minutes: Add any minutes carried over from the seconds column to the sum of the minutes. If this new sum of minutes is 60 or greater, divide the total minutes by 60. The remainder is the final minutes value, and the quotient is carried over and added to the degrees column.
• Degrees: Add any degrees carried over from the minutes column to the sum of the degrees. This total is your final degree value.

Example of Adding Degrees, Minutes, and Seconds

Let's add two angles: 25° 45' 30" and 10° 20' 45".

1. Line Up:

   25° 45' 30"
   + 10° 20' 45"
   ----------

2. Add Separately:

   • Seconds: 30 + 45 = 75"
   • Minutes: 45 + 20 = 65'
   • Degrees: 25 + 10 = 35°

   Initial Sum: 35° 65' 75"

3. Handle Sums (Carry Over):

   • Seconds: 75" is more than 60". 75 ÷ 60 = 1 with a remainder of 15.
     • Final Seconds: 15"
     • Carry over 1 minute.
   • Minutes: Add carried minute: 65' + 1' = 66'. 66' is more than 60'. 66 ÷ 60 = 1 with a remainder of 6.
     • Final Minutes: 06'
     • Carry over 1 degree.
   • Degrees: Add carried degree: 35° + 1° = 36°.
     • Final Degrees: 36°

4. Final Result: 36° 06' 15"

This structured approach ensures that each part of the angular measurement is added correctly, accounting for the base-60 system of minutes and seconds.