# Angle Measures – degrees, minutes and seconds 128-2.2 This video is provided as supplementary
material for courses taught at Howard Community
College and in this video I’m going to talk about adding and subtracting angles which are
measured in degrees, minutes and seconds. So you know that angles are measured in
degrees. We might have an angle which is, let’s say, 35 degrees. Now degrees can be broken
down into smaller units. So one degree can be broken down
into 60 units called minutes. So one degree
equals 60 minutes. Just as we have a symbol to designate, to
show that we’re dealing with degrees, we have that little circle that we put after the number, there’s a symbol we’re going to use to show
that we’re dealing with minutes. And that’s an apostrophe that we put
after the number. Okay, so one degree equals 60minutes. Now minutes can be broken down into
smaller units. We can break one minute into 60
smaller units that we call seconds. And the symbol
for seconds is going to be two apostrophes after the number. So this should be pretty easy to
remember: one degree is 60 minutes, and you think of that the same way you remember that one hour is 60 minutes. One minute is 60 seconds. So, with that information, we’re going to try an
measured in degrees, minutes and seconds. So the first step is
going to be to write those numbers one under the other. So I’ve got 17 degrees, 45 minutes and 28 seconds, and directly under that I’ll put the other
angle, 3 degrees, 31 minutes and 52 seconds. And I’m going to add the each of those kinds of units separately. So I’ll add degrees first. I’ve got 17 and 3, so that’s 20 degrees. Now I’ll go on to the minutes.
I’ve got 35 minutes and 31 minutes, so that’s 76 minutes. And I’ve got 28
seconds plus 52 seconds is going to be 80 seconds. Now I can’t leave that 80 seconds the way it is because that’s
more than one minute. So what I’m going to do is
subtract a minute from it. I’m going to subtract 60 seconds,
which is one minute. And to make up for taking that minute away, I’m
going to add a minute underneath
where I’ve got the minutes written. So I’m subtracting 60 seconds — which is subtracting one minute — and I’m
adding one minute. I’ll do the addition. I’ve got 20 degrees, and then 76 minutes
plus 1 minute is 77 minutes, and then 80 seconds minus 60 seconds is 20 seconds.
I also can’t leave the minutes the way they are. I’ve got 77 minutes. So I’m going to subtract one degree.
I’ll subtract that in the form of 60 minutes, and I’ll add one degree where I’ve got the other degree units. I’ll do that addition. 20 degrees plus one degree is 21 degrees, 77 minutes minus 60 minutes is going to be 17
minutes, and 20 seconds remains 20 seconds.
So this is going to be 21 degrees 17 minutes 20 seconds. Once again, what I did was I lines these angles up so the
degrees, minutes and seconds were above each other. I added each unit separately, the degrees, minutes and seconds.
Then I looked at the seconds and I had 80 seconds. That’s more than one minute so I subtracted a minute in the form of
60 seconds. To make up for that subtraction I added a minute in my minutes column.
That got me down to 20 seconds. But then I had 77 minutes in the minutes
column. So I subtracted one degree in the
fore of 60 minutes. To make up for that subtraction,
I added one degree in the degrees column, and
that gave me my answer. Let’s try a subtraction problem now. So for this problem I’ve got 95 degrees 39 minutes, 28 seconds and I want to subtract 27 degrees, 52 minutes, 56 seconds. So I’ll line these two angles up.
I’ll line their degrees up one under the other, and the
minutes and seconds. So I’ve got 95 degrees, 39 minutes and 28 seconds. And right below that I’m going to
be subtracting 27 degrees, 52 minutes and 56 seconds. So I want to start with the seconds. I’m trying to subtract 28 seconds minus 56 seconds. Now 56 is larger than 28, so I’m going
to have to borrow from the minutes column. When I do that I’m going to
borrow one minute. So instead of 39 minutes, I’m going to cross that out and make that
38 minutes. One minute is 60 seconds,
so I’ll add 60 seconds to the 28 seconds that I have. 60 plus 28 is 88. So now I’ve got 88 seconds and now I can
subtract 88 seconds minus 56 seconds. is 32 seconds. I’ll go on to the minute. I want to subtract 38 minutes minus 52 minutes. 52 is bigger than 38, so I want to
borrow from the degrees. I’ll borrow one degree. I’ll take that
95 degrees and borrow one from it, so that’s going to
become 94 degrees. The one degree that I borrowed is
the same as 60 minutes, so I’ll add 60 minutes to the 38 minutes
that I have and that will get me to 98 minutes. And now I can subtract 98 minutes minus
52 minutes. That’s going to be 46 minutes. And then going over to the degrees, I’ve got 94 degrees and I want to subtract 27. So that’s going to be 67 degrees. So I’ll have 67 degrees 46 minutes 32 seconds. Let me repeat those steps
again. I took the two angle measurements
that I had. I wrote them one under the other.
Then, starting in the seconds column, I see if I can subtract. If I can’t
subtract because the number I’m subtracting is
larger than the number I’m subtracting from, I borrow a minute from the minutes
column, which means I take whatever
number of minutes I had there and decreases it by one, and I add 60
seconds, since one minute equals 60 seconds. So I
added 60 seconds to the amount of seconds I had, and that let me subtract. Then I go to the
minutes column and I see if I have the same problem. If
I can’t subtract there, what I’m going to do is borrow a degree
from the degrees column. So I take the number of degrees,
decrease that one, and add 60minutes,
which is the same as one degree, in the minutes column. I do my
subtraction, go over to his degrees column, and do
the subtraction I have there. And that gives me the answer. So
that’s basically how this works. Take care, I’ll see you next time.