Astronomers sometimes use angle measures divided into degrees, minutes, and seconds. One degree is equal to 60 minutes, and one minute is equal to 60 seconds. Suppose that ∠J and ∠K are complementary and that the measure of ∠J is 45 degrees, 30 minutes, 14 seconds. What is the measure of ∠K? The measure of ∠K is degrees, minutes, and seconds.

Here's what you need to know to answer this question:

            If two angles are "complementary"

            then they add up to 90 degrees.

So now you know that

                                    (Angle-J) + (Angle-K) = 90 degrees .

Subtract (Angle-J)

from each side:                              Angle-K = (90 degrees) - (Angle-J)

    Angle-K  =  (90 degrees) minus (48 degrees 26 minutes 8 seconds)

As soon as you do that subtraction, you have the answer.

The thing that makes it tough is subtracting some minutes

and some seconds from 90 degrees.

How you do that is:  An unusual kind of regrouping ('borrowing').

Usually, when you regroup, you take '1' from a place and use it

to make '10' in the smaller place.

This time, when you take '1' from a place, it gives you '60'

in the smaller place.

-- Take 1 degree away from the 90 degrees.

   Use it to make minutes.

   Then you have                  89 degrees  60 minutes .

-- Take 1 minute away from the 60 minutes.

   Use it to make seconds.

   then you have                    89 degrees  59 minutes  60 seconds .

Now the subtraction is a lot easier.

            89 degrees  59 minutes  60 seconds

minus   48 degrees  26 minutes    8 seconds .

That's easy to do, and the difference is the measure of Angle-K.

Step-by-step explanation:

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!