Question

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.

Answer 1

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.

Explanation: