SOLUTION: The supplement of an angle is 10deg. smaller than three times its complement. Find the size of the angle. answer= 40 deg. please show me step by step how to solve

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Question 175903This question is from textbook
:
The supplement of an angle is 10deg. smaller than three times its complement. Find the size of the angle.
answer= 40 deg. please show me step by step how to solve This question is from textbook

Found 2 solutions by EMStelley, jim_thompson5910:
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
First -
2 angles are complementary if their sum is 90 degrees
2 angles are supplementary if their sum is 180 degrees
Call the angle we are looking for x. Then it's complement is 90-x and its supplement is 180-x. (To see this think about an example - say x is 30 degrees. Then its complement is 90-30=60 degrees and its supplement is 180-30=150 degrees.)
So, if the supplement of x is 10 degrees smaller than three times its complement, we can represent that by
180-x=3%2890-x%29-10
So, first, lets distribute through on the right hand side and group like terms.
180-x=270-3x-10
180-x=260-3x
Now, we need to solve for x. First, we could add 3x to both sides.
180%2B2x=260
Now, subtract 180 from both sides.
2x=80
Lastly, dividing both sides by 2, we get that x=40.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=given angle, y=supplement of angle x, and z=complement of angle x


Because "The supplement of an angle is 10deg. smaller than three times its complement.", this tells us that y=3z-10


Since "y" is the supplement to angle x, this means x%2By=180.


Also, since "z" is the complement to angle x, this means x%2Bz=90. Solving for "z" and we get z=90-x


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x%2By=180 Start with the second equation.


x%2B3z-10=180 Plug in y=3z-10 (the first equation)


x%2B3%2890-x%29-10=180 Plug in z=90-x (the third equation)



Notice that after all of these substitutions, we end up with a simple equation with one unknown.


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So let's solve the equation:


x%2B3%2890-x%29-10=180 Start with the given equation.


x%2B270-3x-10=180 Distribute.


-2x%2B260=180 Combine like terms on the left side.


-2x=180-260 Subtract 260 from both sides.


-2x=-80 Combine like terms on the right side.


x=%28-80%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=40 Reduce.


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Answer:

So the answer is x=40 which means that the given angle is 40 degrees.