SOLUTION: The complement of angle A is 20 degrees less than half the supplement of angle A. Find the measure of angle A. Where do I start from here.

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Question 207726This question is from textbook Advanced Mathematics An Incremental Development
: The complement of angle A is 20 degrees less than half the supplement of angle A. Find the measure of angle A. Where do I start from here. This question is from textbook Advanced Mathematics An Incremental Development

Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let

A = measure of angle A
c = measure of complement angle
s = measure of supplement angle


"The complement of angle A is 20 degrees less than half the supplement of angle A" literally translates to the equation c=%281%2F2%29s-20


Also, by definition, since 'c' is the complement to angle A, this means that they add to 90 degrees. So A%2Bc=90

Furthermore, supplemental angles add to 180 degrees. Because 's' is the supplement to angle A, we know that A%2Bs=180


A%2Bc=90 Start with the second equation.


c=90-A Subtract A from both sides.


A%2Bs=180 Move onto the second equation


s=180-A Subtract A from both sides.


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c=%281%2F2%29s-20 Now move back to the first equation.


90-A=%281%2F2%29s-20 Plug in c=90-A


90-A=%281%2F2%29%28180-A%29-20 Plug in s=180-A


90-A=%281%2F2%29%28180%29-%281%2F2%29A-20 Distribute


90-A=180%2F2-%281%2F2%29A-20 Multiply


90-A=90-%281%2F2%29A-20 Reduce


2%2890%29-2%28a%29=2%2890%29-cross%282%29%28%281%2Fcross%282%29%29a%29-2%2820%29 Multiply EVERY term by the LCD 2 to clear any fractions.


180-2a=180-1a-40 Multiply and simplify.


180-2a=-a%2B140 Combine like terms on the right side.


-2a=-a%2B140-180 Subtract 180 from both sides.


-2a%2Ba=140-180 Add a to both sides.


-a=140-180 Combine like terms on the left side.


-a=-40 Combine like terms on the right side.


a=%28-40%29%2F%28-1%29 Divide both sides by -1 to isolate a.


a=40 Reduce.


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Answer:

So the solution is a=40


This means that the original angle is 40 degrees while the complement is c=90-40=50 degrees and the supplement is s=180-40=140 degrees.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

The complement of angle A is 20 degrees less than half the supplement of angle A. Find the measure of angle A. Where do I start from here.

The complement of angle A is: (90 - A)

The supplement of angle A is: (180 - A)

Since the complement of A is 20 degress less than half the supplement of angle A, then we have:

%2890+-+A%29+%2B+20+=+%281%2F2%29%2A%28180+-+A%29

110+-+A+=+%28180+-+A%29%2F2

Cross-multiplying, we get: 2(110 - A) = 180 - A

220 - 2A = 180 - A
- 2A + A = 180 - 220

- A = - 40
A+=+%28-40%29%2F-1

A = 40

Therefore, angle A = highlight_green%2840%29 degrees.