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) (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
Also, by definition, since 'c' is the complement to angle A, this means that they add to 90 degrees. So
Furthermore, supplemental angles add to 180 degrees. Because 's' is the supplement to angle A, we know that
Start with the second equation.
Subtract A from both sides.
Move onto the second equation
Subtract A from both sides.
----------------------------------------------
Now move back to the first equation.
Plug in
Plug in
Distribute
Multiply
Reduce
Multiply EVERY term by the LCD to clear any fractions.
Multiply and simplify.
Combine like terms on the right side.
Subtract from both sides.
Add to both sides.
Combine like terms on the left side.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
----------------------------------------------------------------------
Answer:
So the solution is
This means that the original angle is 40 degrees while the complement is degrees and the supplement is degrees.
Answer by MathTherapy(10555) (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:
Cross-multiplying, we get: 2(110 - A) = 180 - A
220 - 2A = 180 - A
- 2A + A = 180 - 220
- A = - 40
A = 40
Therefore, angle A = degrees.
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