SOLUTION: An angle measures 28° more than the measure of its complementary angle. What is the measure of each angle?

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Question 1153316: An angle measures 28° more than the measure of its complementary angle. What is the measure of each angle?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39628)   (Show Source): You can put this solution on YOUR website!
This was answered yesterday.
A very similar problems was answered yesterday.


https://www.algebra.com/algebra/homework/Angles/Angles.faq.question.1153253.html
Answer by ikleyn(52866)   (Show Source): You can put this solution on YOUR website!
.

Let the angle measure be x degrees.


Then the measure of its complementary angle is 90°-x.


We are given that


    x = (90-x) + 28.


Solve it for x


    x + x = 90 + 28

    2x    = 118

     x    = 118/2 = 59.


ANSWER.  The angle measure is 59°.  The complementary angle measure is 90°-59° = 31°.


CHECK.   59° - 31° = 28°.    ! Precisely correct !

Solved.

------------

@josgarithmetic, yesterday you solved different problem under that link.



Answer by greenestamps(13206)   (Show Source): You can put this solution on YOUR website!


Of course a formal algebraic solution is valid; and you should know how to do it.

If an algebraic solution is not required, here is a strategy that can be used to solve problems like this quickly with a little mental arithmetic.

You know the sum of the two angles is 90 degrees.
If the two angles were each 45 degrees, the difference would be 0.
To make the two angles differ by 28 degrees, take the two 45 degree angles and add 14 degrees to one of them and subtract 14 degrees from the other, giving you the answer: 45+14 = 59 degrees and 45-14 = 31 degrees.

To further demonstrate this strategy, here is another very basic problem for which it can be used:

The sum of two numbers is 84; their difference is 16. Find the numbers.

84/2 = 42; 42+42 = 84. The difference between 42 and 42 is 0.
16/2 = 8; the two numbers 42+8=50 and 42-8=34 have the same sum of 84 and a difference of 16.
Answer: 50 and 34.
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