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

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) (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

So, first, lets distribute through on the right hand side and group like terms.

Now, we need to solve for x. First, we could add 3x to both sides.

Now, subtract 180 from both sides.

Lastly, dividing both sides by 2, we get that x=40.
Answer by jim_thompson5910(35256) (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

Since "y" is the supplement to angle x, this means .

Also, since "z" is the complement to angle x, this means . Solving for "z" and we get

----------------------------------------------------

Start with the second equation.

Plug in (the first equation)

Plug in (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:

Start with the given equation.

Distribute.

Combine like terms on the left side.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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Answer:

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

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