Final answer:
The difference between the angles 60° 50' 40" and 30° 40' 50" is 30° 9' 50". To find this, we subtract each unit of the angle, borrowing from the next largest unit when needed.
Step-by-step explanation:
To subtract two angles measured in degrees, minutes, and seconds, we start by subtracting the smallest unit first and then, if necessary, borrow from the next larger unit.
Let's subtract 30 degrees, 40 minutes, and 50 seconds from 60 degrees, 50 minutes, and 40 seconds:
First subtract the seconds:
40 seconds - 50 seconds cannot be done without borrowing, so we take 1 minute (which is 60 seconds) from the minutes. The equation becomes 50 minutes and 40 seconds + 60 seconds = 50 minutes and 100 seconds.
Now we can subtract:
100 seconds - 50 seconds = 50 seconds.
Since we borrowed 1 minute from the minutes, we now have 49 minutes to work with. So subtract the minutes:
49 minutes - 40 minutes = 9 minutes.
Finally, subtract the degrees:
60 degrees - 30 degrees = 30 degrees.
The difference between the two angles is 30 degrees, 9 minutes, and 50 seconds.
To convert units of time, such as converting 120 seconds to minutes, we divide by 60 since there are 60 seconds in a minute. Therefore, 120 seconds is equal to 2 minutes.