 Hello and welcome to the session. In this session we will discuss how to add and subtract the measurement of angles. In our earlier session, we have discussed about degree minute second measure and decimal degree measure of angles. Let us now recall the relation between degree minute and second. It is as follows. 1 degree is equal to 60 minutes or 1 minute is equal to 1 by 60 degrees and 1 minute is equal to 60 seconds or 1 second is equal to 1 by 60 minutes. Now we will discuss how to add and subtract the angles in degree minute second. First of all let us discuss addition of angles. Now let us consider the following example that is add 37 degrees 39 minutes and 83 degrees 36 minutes. Now to add these angle measurements we write them in columns degree measure in first column that is 37 degrees and 83 degrees and minute measure in second column that is 39 minutes and 36 minutes and we will add the corresponding numbers that is we will add the degrees and minutes separately. Now we add minutes first that is 9 plus 6 which is equal to 15 so we write 5 and 1 above 3 and now we add 1 plus 3 plus 3 that is 7 so we write 7 so we have 75 minutes now we add degrees 7 plus 3 is 10 so we write 0 and we write 1 above 3 and now 1 plus 3 plus 8 that is 12 so we write 12 and we have 120 degrees so we write 37 degrees 39 minutes plus 83 degrees 36 minutes is equal to 120 degrees 75 minutes now we know that 1 degree is equal to 60 minutes so here 75 minutes can be written as 60 minutes plus 15 minutes that is equal to 1 degree plus 15 minutes so we carry 1 degree from minutes column to degree column and therefore we get 120 degrees 75 minutes is equal to 121 degrees 15 minutes thus we can say that 37 degrees 39 minutes plus 83 degrees 36 minutes is equal to 121 degrees 15 minutes so we conclude that to add the angles we will align degrees with degrees minutes with minutes and seconds with seconds then we will add degrees minutes and seconds respectively and we should always take into consideration 1 degree is equal to 60 minutes and 1 minute is equal to 60 seconds for example 63 seconds can be written as 1 minute 3 seconds and 64 minutes can be written as 1 degree 4 minutes now we are going to discuss subtraction of angles to subtract angles in degree minute measure we will borrow 1 degree from degrees given and add it to the given minute when needed using the rule 1 degree is equal to 60 minutes if seconds are also given then we will borrow 1 minute from the minutes given and added to the given seconds when needed using the result 1 minute is equal to 60 seconds after performing these steps we will subtract the two numbers let us consider an example subtract 53 degrees 36 minutes 42 seconds from 90 degrees now see 90 degrees can be written as 90 degrees 00 minutes 00 seconds since we have to subtract from 90 degrees so we will borrow 1 degree from 90 degrees first and add it to the given 00 minutes because 00 is smaller than 36 so we cannot subtract the two numbers unless we have a larger number than 36 so we get 90 degrees 00 minutes 00 seconds minus 1 degree and plus 60 minutes so we get 89 degrees 60 minutes and 00 seconds since we are also given seconds so now we will borrow 1 minute from 60 minutes and add it to the given 00 seconds using the result 1 minute is equal to 60 seconds because 00 seconds are smaller than 42 seconds so we cannot subtract directly so we get 89 degrees 60 minutes 00 seconds minus 1 minute and plus 60 seconds and this is equal to 89 degrees 59 minutes 60 seconds so now we have 90 degrees is equal to 89 degrees 59 minutes 60 seconds so now we will subtract 53 degrees 36 minutes 42 seconds from 89 degrees 59 minutes 60 seconds so we first align degrees with degrees minutes with minutes and seconds with seconds that is in the first column we write degrees in the second column we write minutes in the third column we write seconds and now we subtract starting from seconds now here we have 0 minus 2 since 0 is smaller than 2 so here we replace 0 by 10 and here we replace 6 by 5 and we have 10 minus 2 that is 8 and 5 minus 4 that is 1 so we have 60 seconds minus 42 seconds that is equal to 18 seconds now we subtract minutes and here we have 9 minus 6 that is 3 and 5 minus 3 that is 2 so we have 59 minutes minus 36 minutes that is equal to 23 minutes and then we subtract degrees that is 9 minus 3 which is equal to 6 and 8 minus 5 that is 3 so we have 89 degrees minus 53 degrees which is equal to 36 degrees thus we get 90 degrees minus 53 degrees 36 minutes 42 seconds is equal to 36 degrees 23 minutes 18 seconds now we should note that if only minutes and degrees are given in angle measure then we will not take seconds into consideration while subtracting for example if we have to subtract 32 degrees 53 minutes from 90 degrees then we will not take seconds while subtracting because they are not given in the angle measure we will directly borrow 1 degree and subtract so we get 90 degrees is equal to 89 degrees 60 minutes and we have 89 degrees 60 minutes minus 32 degrees 53 minutes and now we subtract starting from minutes here we have 0 minus 3 since 0 is smaller than 3 so we replace 0 by 10 and 6 by 5 and here we have 10 minus 3 that is 7 and 5 minus 5 that is 0 so we have 60 minutes minus 53 minutes that is equal to 7 minutes now we subtract degrees and we have 9 minus 2 that is 7 and 8 minus 3 that is 5 so we have 89 degrees minus 32 degrees which is equal to 57 degrees so 89 degrees 60 minutes minus 32 degrees 53 minutes is equal to 57 degrees 7 minutes thus we have 90 degrees minus 32 degrees 53 minutes is equal to 57 degrees 7 minutes thus in this session we have discussed how to add and subtract the measurement of angles this completes our session hope you enjoyed this session