SOLUTION: I need help setting up the following problem. The measure of angle A is half the difference between its complement and supplement. Find the measure of angle A. Thank you!

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Question 503883: I need help setting up the following problem.
The measure of angle A is half the difference between its complement and supplement. Find the measure of angle A.
Thank you!
Found 3 solutions by Theo, ikleyn, josgarithmetic:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the following picture shows you how to solve this problem.
look below the picture for comments.
$$$$$
number 1:
A is the angle, 90 - A is the complement of the angle, 180 - A is the supplement of the angle.
number 2:
the formula from your problem statement is as shown.
the difference between the supplement and the complement is within the parentheses.
the supplement is subtracting the complement because the supplement will be bigger than the complement.
number 3:
the formula from number 2 is simplified by multiplying what is in the parentheses by 2 using the distributive law of multiplication.
number 4:
the formula from number 3 is simplified further by removing any remaining parentheses.
number 5:
you get our answer by simplifying the equation from number 4 by combining like terms.
the A/2 cancels out because of a minus and a plus of the same value.
number 6:
this is a check to see that the equation was solved properly.
we just substitute the values we discovered in the original formula to prove that the formula is true when we do that.
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.
The measure of angle A is half the difference between its complement and supplement.
Find the measure of angle A.
~~~~~~~~~~~~~~~~~~~~~~~~~~ 


The measure of the complement angle is 90-A degrees.


The measure of the supplement angle is 180-A degrees.


The difference between the supplement angle measure and the complement angle measure is

    (180-A) - (90-A) = 90 degrees.


Half of this difference is 45 degrees.


Hence, the measure of angle A is 90/2 = 45 degrees.

Solved.



Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!






Does this make any sense?
complement, 45.
supplement, 135.
Original statement,
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