SOLUTION: if the suppliment of an angle is 20 more than 2 times its compliment, what is the original angle, its compliment, and its suppliment

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Let

x = measure of unknown angle
y = measure of complement angle to angle 'x'
z = measure of supplement angle to angle 'x'


Since we know that 'x' and 'y' are complement angles (ie the angles add to 90 degrees), this means . Likewise, 'x' and 'z' are supplement angles (the angles add to 180 degrees), so .


Furthermore, we're told that we have an "angle whose supplement measures 20 more than twice its compliment" which means that


Start with the first equation.


Subtract x from both sides.

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Move onto the second equation.


Subtract x from both sides.

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Move to the third equation.


Plug in


Plug in


Distribute.


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.


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Answer:

So the solution is


This means that the unknown angle is 20 degrees.


So the complement is degrees


and the supplement is degrees.