Measurement of Angles Level 5 In this video we will continue going over
slightly more challenging examples involving parts of a degree.
Let’s take a look at the first example.
Change 15 and two ninths degrees to degrees, minutes, and seconds.
In this problem we are asked to change the degree measurement that contains a fractional
part of a degree into the degrees minutes and seconds notation.
Notice that instead of a decimal we have a fraction.
Usually when the fractional portion of a degree has a decimal representation that terminates
then we write it out.
In this case the decimal representation of two ninths repeats forever and ever so we
leave it as a fraction.
Alright similar to the previous problems we want to convert the fractional portion of
the degree into minutes so we take the fraction and multiply it by 60 doing that we obtain
13 and a third minutes, since we also have a fractional portion of a minute we go ahead
and convert this fraction into seconds by multiplying it by 60 once more doing that
we obtain the following.
So 15 and two ninths degrees can be written as 15 degrees 13 minutes 20 seconds and this
is our final answer.
Let’s take a look at the next problem.
Change 72 degrees 22 minutes 30 seconds to degrees.
In this problem we need to convert the following angle written in degrees-minutes-seconds into
degrees.
Recall that we need to convert the minutes and seconds into an equivalent degree measurement
and add them with the integer degree measurement.
So in order to convert the minutes we divide them by 60 and in order to convert the seconds
we divide them by 3600.
This way we obtain an equivalent fractional degree measurement for the minutes and seconds.
Now it is just a matter of adding the fractional form of the minutes and seconds with the integer
degree measurement.
We can simplify the fraction representing the seconds as follows, and then we can add
both fractions by finding a common denominator and rewriting the fraction representing the
minutes.
Adding the fractions we obtain the following.
Now it is just a matter of reducing the fraction doing that we obtain 72 and three eights degrees
or 72.375 degrees.
So this is our final answer.
Alright let’s move along to slightly more challenging examples.
Evaluate 49 degrees 32 minutes 55 seconds plus 37 degrees 27 minutes 15 seconds.
In this problem we are given two angle measures and we are asked to find the sum of these
angle measurements.
We can add angles similar to the way we add numbers by aligning them in a vertical column
and adding the seconds, minutes and degrees of each angle with one another.
In this case we would first add the seconds followed by the minutes and lastly we add
the degrees of each angle.
Next we need to modify our result so that it is consistent with the degrees-minutes-seconds
notation.
Notice that we have 70 seconds in our answer recall that there are 60 seconds in one minute
this means that we have an excess amount of seconds specifically we have an excess of
10 seconds so to fix this we are going to exchange 60 seconds and convert it into one
minute and add this single minute to the minutes place while keeping what’s left in the seconds
place in this case 10 seconds.
Now we currently have 59 minutes in our answer, adding one additional minute from the seconds
place will bump this value to 60 minutes.
Recall that 1 degree is equivalent to 60 minutes since we have enough minutes to create 1 degree
we go ahead and exchange the 60 minutes for 1 degree leaving us with 0 minutes.
Notice that we have 86 in the degrees place but because we converted 60 minutes into 1
degree we now have 87 degrees.
In the end, the sum of these two angle measurements simplifies to 87 degrees 10 seconds and this
is our final answer.
Notice that we need to convert any excess part of a minute or second when simplifying
an angle measure written in this notation.
Alright let’s try a subtraction problem.
Evaluate 90 degrees minus 67 degrees 21 minutes 37 seconds.
In this problem we are given two angle measures and we are asked to subtract them.
Similar to addition of angle measurements we can subtract angles written in degrees
minutes and seconds by aligning the angle measures in a vertical column and subtracting
the seconds, minutes and degrees from each angle measure.
Before we can do this we have to rewrite 90 degrees so that it includes minutes and seconds.
Initially 90 degrees has 0 minutes and 0 seconds, since we cannot subtract 37 seconds from zero
seconds and 21 minutes from 0 minutes we need to rewrite the measurement of the first angle
so that we can carry out the subtraction.
Similar to the way we borrowed when subtracting real numbers when the top digit was smaller
than the bottom digit, we need to borrow from the degrees place and convert 1 degree into
minutes and at times we also need to convert 1 minute into 60 seconds.
We are first going to borrow a degree and convert it into 60 minutes as follows this
reduces the degrees place to 89 and changes the minutes place to 60.
Next we need to borrow a minute and convert it into 60 seconds this reduces the minutes
place to 59 and changes the seconds place to 60.
Now that we have rewritten 90 degrees into this equivalent form we proceed with the subtraction.
So we subtract the seconds, minutes and degrees from each angle as follows.
In the end the difference is equal to 22 degrees 38 minutes 23 seconds and this is our final
answer.
Keep in mind that we are able to borrow degrees or minutes in order to rewrite the angle measurement
into a subtraction friendly form.
Alright in our next video we will go over more examples involving parts of a degree
and congruent angles.