SOLUTION: The supplement of an angle is 30 deg. larger than twice its complement. Find the measure of the angle. Answer = 30 deg. Please show me step by step how to solve. Thank you.

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Question 175904This question is from textbook elementary algebra
: The supplement of an angle is 30 deg. larger than twice its complement. Find the measure of the angle.
Answer = 30 deg. Please show me step by step how to solve.
Thank you. This question is from textbook elementary algebra

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 30 deg. larger than twice 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

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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 tells us that the original angle is 30 degrees.