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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Question 215106: if the suppliment of an angle is 20 more than 2 times its compliment, what is the original angle, its compliment, and its suppliment
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 x%2By=90. Likewise, 'x' and 'z' are supplement angles (the angles add to 180 degrees), so x%2Bz=180.


Furthermore, we're told that we have an "angle whose supplement measures 20 more than twice its compliment" which means that z=2y%2B20


x%2By=90 Start with the first equation.


y=90-x Subtract x from both sides.

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x%2Bz=180 Move onto the second equation.


z=180-x Subtract x from both sides.

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z=2y%2B20 Move to the third equation.


z=2%2Ahighlight%28%2890-x%29%29%2B20 Plug in y=90-x


highlight%28180-x%29=2%2890-x%29%2B20 Plug in z=180-x


180-x=180-2x%2B20 Distribute.


180-x=-2x%2B200 Combine like terms on the right side.


-x=-2x%2B200-180 Subtract 180 from both sides.


-x%2B2x=200-180 Add 2x to both sides.


x=200-180 Combine like terms on the left side.


x=20 Combine like terms on the right side.


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Answer:

So the solution is x=20


This means that the unknown angle is 20 degrees.


So the complement is y=90-x=90-20=70 degrees


and the supplement is z=180-x=180-20=160 degrees.