SOLUTION: Trouble setting this up. Half the supplement of the angle is 12 degrees less than twice the complement of the angle. Find the measure of the angle. Thank You in advance for your

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Question 162875This question is from textbook mathemathical ideas
: Trouble setting this up.
Half the supplement of the angle is 12 degrees less than twice the complement of the angle. Find the measure of the angle.
Thank You in advance for your help.
George This question is from textbook mathemathical ideas

Found 2 solutions by nerdybill, Earlsdon:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
Remember, if two angles are "supplementary" then the sum of the two angles is 180. And, if two angles are "complementary" then the sum of the two angles is 90.
.
Let x = "the angle"
then
180-x = the supplement
90-x = the complement
.
From: "Half the supplement of the angle is 12 degrees less than twice the complement of the angle."
.
(1/2)(180-x) = 2(90-x) - 12
180-x = 4(90-x) - 24
180-x = 360 -4x - 24
180-x = 336 -4x
180+3x = 336
3x = 156
x = 52 degrees

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Let the angle you want to find = A.
The supplement of angle A is .
Half the supplement of angle A is
The complement of angle A is .
Twice the complement of angle A is and 12 degrees less than that is .
Now let's put it all together as described in the problem statement!
Now we can solve for the unknown angle A. First, multiply both sides of this equation by 2 to clear the fraction.
Expand (distributive property) the right-hand side.
Simplify.
Add A to both sides.
Subtract 336 from both sides.
Finally, divide both sides by -3.

The measure of the angle A is 52 degrees.